WASHINGTON--Sen. John McCain (R-Ariz.) and other opponents of filibuster reform plan to offer a counterproposal to the Senate on Friday, McCain told The Huffington Post. The group plans to present their proposal to their parties to gauge support for the idea, he said.

McCain would not offer any details about the proposal. Sen. Chuck Schumer (D-N.Y.), Sen. Lindsey Graham (R-S.C.), Sen. Lamar Alexander (R-Tenn.), Sen. Jon Kyl (R-Ariz.), Sen. Carl Levin (D-Mich.) and Sen. Mark Pryor (D-Ark.) are also involved in it.

Alexander, emerging from a bipartisan meeting of reform opponents held this morning in Kyl's office, said that the proposal would limit the use of the filibuster in some cases, such as on a motion to proceed to debate, and also include provisions allowing for amendments for the minority.

"We have so many new members of the Senate, about half of the senators have never seen the Senate work properly because they've only been here five or six years," Alexander said. "So we're trying to get back to the days when the motion to proceed wasn't used to block so many bills and when the majority leader allowed senators to offer almost any amendment. Most of that has to be established by practice, by good behavior, rather than by changing the rules."

Alexander added that the group has briefed both Reid and Senate Minority Leader Mitch McConnell (R-Ky.) on their proposal. "It's now up to the leaders to decide what they want to do," he said.

Unexpectedly, Sen. Ben Cardin (D-Md.), whose fellow Senate class of 2006 colleagues are generally supportive of significant filibuster reform, also emerged from Kyl's office following the meeting. Asked by HuffPost if he was part of the bipartisan group, he said simply: "I'm part of the Senate, yes."

The Democratic members of the anti-reform group will also brief their colleagues today, a source told HuffPost.

The proposal needs a 2/3 majority to pass and avoid the so-called nuclear option -- changing the rules by a simple majority vote. Asked if he had the votes, McCain said, "I hope so."

Levin said the goal was to stave off the "talking filibuster" proposal by Sen. Jeff Merkley (D-Ore.). Merkley is proposing to restore the filibuster to what many think of it as -- one senator holding up the entire Senate floor, as Jimmy Stewart did in "Mr. Smith Goes To Washington."

Now, senators need only raise their hand to force legislation to need 60 votes.

Advocates of the "talking filibuster," however, are close to a majority needed to reform the rules. Progressive and labor organizations are backing the proposal. (Here is a whip count of the votes.)

Restoring the traditional filibuster has broad public support -- a HuffPost/YouGov poll found that by a 65-9 margin, Americans favor senators having to actively debate to oppose legislation.

UPDATE 3:43 p.m. -- Sen. Maria Cantwell (D-Wash.), emerging from a caucus-wide meeting on filibuster reform, told HuffPost, "There's 51 votes to do something, that's for sure." Levin and Pryor, meanwhile, returned to Kyl's office after the meeting to plot further opposition to filibuster reform. Levin and McCain, notably, are calling themselves "a group of eight" rather than a "gang of eight." Perhaps surprisingly, that's a meaningful distinction in the Senate: A group is considered to be less of a cohesive and determined force than a gang. The group's proposal is not a rules change, but rather a "standing order" that would expire next term, according to a copy of the proposal.

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  • Robert Byrd (D-W.V.)

    <strong>Dates of service:</strong> Jan. 3, 1959 to June 28, 2010 <strong>Years of service:</strong> 51 years, 5 months, 26 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Robert Byrd, D-W.V., appears at a Senate hearing on May 9, 2007 in Washington. He died on June 28, 2010 at the age of 92. (KAREN BLEIER/AFP/Getty Images)

  • Daniel Inouye (D-Hawaii)

    <strong>Dates of service:</strong> Jan. 3, 1963 to Dec. 17, 2012 <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Senate Appropriations Defense Subcommittee Chairman Daniel Inouye (D-HI) speaks at a May 18, 2011 hearing in Washington. (Chip Somodevilla/Getty Images)

  • Strom Thurmond (R-S.C.)

    <strong>Dates of service:</strong> Dec. 14, 1954 to April 4, 1956 and Nov 7, 1956 to Jan 3, 2003 <strong>Years of service:</strong> 47 years, 5 months, 8 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Senator Strom Thurmond, R-S.C., pictured on May 22, 1997. He died on June 26, 2003 at the age of 100. (STEPHEN JAFFE/AFP/Getty Images)

  • Edward Kennedy (D-Mass.)

    <strong>Dates of service:</strong> Nov. 7, 1962 to Aug. 25, 2009 <strong>Years of service:</strong> 46 years, 9 months, 19 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Edward Kennedy (D-Mass.) speaks during a Jan. 21, 2007 taping of NBC's "Meet the Press." He died on Aug. 25, 2009 at the age of 77. (Photo by Alex Wong/Getty Images)

  • Carl Hayden (D-Ariz.)

    <strong>Dates of service:</strong> March 4, 1927 to Jan. 3, 1969 <strong>Years of service:</strong> 41 years, 9 months, 30 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> President Lyndon Johnson presents a pen to Sen. Carl Hayden, D-Ariz., on September 30, 1968 in Washington. Hayden died on Jan. 25, 1972 at the age of 94. (AP Photo)

  • John Stennis (D-Miss.)

    <strong>Dates of service:</strong> Nov. 5, 1947 to Jan. 2, 1989 <strong>Years of service:</strong> 41 years, 1 month, 29 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> John Stennis, chairman of the Senate Armed Services Committee, speaks on the July 6, 1969 edition of ABC's "Issues and Answers." Stennis died on April 23, 1995 at the age of 93. (AP Photo)

  • Ted Stevens (R-Alaska)

    <strong>Dates of service:</strong> Dec. 24, 1968 to Jan. 2, 2009 <strong>Years of service:</strong> 40 years, 10 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> In this Tuesday, April 7, 2009 file photo, former Sen. Ted Stevens arrives at federal court in Washington. Stevens died in a plane crash on Monday, Aug. 9, 2010 at the age of 86. (AP Photo/Gerald Herbert, file)

  • Patrick Leahy (D-Vt.)

    <strong>Dates of service:</strong> Jan. 3, 1975 to present <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Patrick Leahy, D-Vt., stands in front of the U.S. Capitol building on Monday, Nov. 26, 2007. (AP Photo/Charles Dharapak)

  • Ernest Hollings (D-S.C.)

    <strong>Dates of service:</strong> Nov. 9, 1966 to Jan. 2, 2005 <strong>Years of service:</strong> 38 years, 1 month, 25 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Ernest Hollings, D-S.C., appears at a Town Hall on Thursday, Oct. 7, 1983. He ran for the 1984 Democratic presidential nomination, but lost out to Vice President Walter Mondale. (AP Photo/Ron Frehm)

  • Richard Russell (D-Ga.)

    <strong>Dates of service:</strong> Jan. 12, 1933 to Jan. 21, 1971 <strong>Years of service:</strong> 38 years, 19 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Richard Russell (D-Ga.), shown from his Senate office desk in Washington on July 14, 1942. Russell died on Jan. 21, 1971 at age 73. (AP Photo/Eugene Abbott)

  • Russell Long (D-La.)

    <strong>Dates of service:</strong> Dec. 31, 1948 to Jan. 2, 1987 <strong>Years of service:</strong> 38 years, 3 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Russell Long, shown at his desk in Baton Rouge, La., on Feb. 21, 1948. Long died on May 9, 2003 at age 84. (AP Photo)

  • Orrin Hatch (R-Utah)

    <strong>Dates of service:</strong> Jan 3. 1977 to present <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> U.S. Sen. Orrin Hatch (R-Utah) heads to a weekly policy meeting at the Capitol on March 20, 2012 in Washington. (Photo by T.J. Kirkpatrick/Getty Images)

  • Francis Warren (R-Wyo.)

    <strong>Dates of service:</strong> Nov. 18, 1890 to March 3, 1893 and March 4, 1895 to Nov. 24, 1929 <strong>Years of service:</strong> 37 years, 4 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> (Photo by Alex Wong/Getty Images)

  • James Eastland (D-Miss.)

    <strong>Dates of service:</strong> June 30, 1941 to Sept. 28, 1941 and Jan. 3, 1943 to Dec. 27, 1978 <strong>Years of service:</strong> 36 years, 2 months, 24 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. James O. Eastland of Mississippi, is shown in Washington on March 25, 1971. Eastland died on Feb. 19, 1986 at age 81. (AP Photo / Charles Tasnadi)

  • Warren Magnuson (D-Wash.)

    <strong>Dates of service:</strong> Dec. 14, 1944 to Jan. 2, 1981 <strong>Years of service:</strong> 36 years, 20 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Then-Rep. Warren Magnuson (D-Wash.) smiles in his Washington office on Oct. 19, 1943. Magnuson died on May 20, 1989 at the age of 84. (AP Photo)

  • Joe Biden (D-Del.)

    <strong>Dates of service:</strong> Jan. 3, 1973 to Jan. 15, 2009 <strong>Years of service:</strong> 36 years, 13 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Democratic vice presidential candidate and U.S. Senator Joe Biden (D-Del.) speaks at a rally in support of then-Democratic presidential nomineee U.S. Sen. Barack Obama (D-IL) on October 12, 2008 in Scranton, Pa. (Photo by Jeff Fusco/Getty Images)

  • Pete Domenici (R-N.M.)

    <strong>Dates of service:</strong> Jan. 3, 1973 to Jan. 2, 2009 <strong>Years of service:</strong> 36 years <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> U.S. Republican Sen. Pete Domenici (R-N.M.) listens during the announcement of the America Competes Act on March 5, 2007 in Washington. (MANDEL NGAN/AFP/Getty Images)

  • Richard Lugar (R-Ind.)

    <strong>Dates of service:</strong> Jan 3. 1977 to Jan. 3, 2013 <strong>Years of service:</strong> 36 years <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Richard Lugar attends a courtesy call to the Malacanang Palace in Manila on October 29, 2012. (NOEL CELIS/AFP/Getty Images)

  • Claiborne Pell (D-R.I.)

    <strong>Dates of service:</strong> Jan. 3, 1961 to Jan. 2, 1997 <strong>Years of service:</strong> 36 years <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> U.S. Sen. Claiborne Pell, D-R.I., announces on Sept. 5, 1995 that he would not seek a seventh term in office. Pell died on Jan. 1, 2009 at age 90. (AP Photo/Charles Krupa) (AP Photo/Charles Krupa, File)

  • Kenneth McKellar (D-Tenn.)

    <strong>Dates of service:</strong> March 4, 1917 to Jan. 2, 1953 <strong>Years of service:</strong> 35 years, 10 months <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Kenneth McKellar (D-Tenn) left, and James M. Landis, OCD director meet on Feb. 27, 1942. McKellar died on Oct. 25, 1957 at age 88. (AP Photo)

  • Milton Young (R-N.D.)

    <strong>Dates of service:</strong> March 12, 1945 to Jan. 2, 1981 <strong>Years of service:</strong> 35 years, 9 months, 22 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Secretary of State Henry Kissinger, left, chats to Senator John L. McClellan (D-Ark.), center, and Senator Milton Young (R-N.D.), at the White House in Washington, March 24, 1975. Young died on May 31, 1983 at the age of 85. (AP Photo)

  • Ellison Smith (D-S.C.)

    <strong>Dates of service:</strong> March 4, 1909 to Nov. 17, 1944 <strong>Years of service:</strong> 35 years, 8 months, 13 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Ellison Smith (left) meets with Secretary of Agriculture, Henry Wallace (right) on Jan. 18, 1934 in Washington. Smith died on Nov. 17, 1944 at age 80. (AP Photo)

  • Allen Ellender (D-La.)

    <strong>Dates of service:</strong> Jan. 3, 1937 to July 27, 1972 <strong>Years of service:</strong> 35 years, 6 months, 24 days <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Sen. Allen Ellender, D-La., bids goodbye to Mrs. Ladybird Johnson after a gumbo luncheon at the Capitol on August 21, 1964. Ellender died on July 27, 1972 at age 81. (AP Photo)

  • William Boyd Allison (R-Iowa)

    <strong>Dates of service:</strong> March 4, 1873 to Aug. 4, 1908 <strong>Years of service:</strong> 35 years, 5 months <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a>

  • Thad Cochran (R-Miss.)

    <strong>Dates of service:</strong> Dec. 27, 1978 to present <strong>Source:</strong> <a href="http://www.senate.gov/senators/Biographical/longest_serving.htm">United States Senate</a> Republican US Senator from Mississippi Thad Cochran attends a joint press conference with US Ambassador to Iraq Zalmay Khalilzad and Iraqi Planning Minister Barhem Saleh (not seen), in Baghdad's Heavily fortified Green Zone, 19 April 2006. (SABAH ARAR/AFP/Getty Images)