WASHINGTON -- House Republicans are fuming at Sen. Ted Cruz (R-Texas) for conceding that the party's efforts to repeal Obamacare aren't going anywhere in the Senate -- and leaving the House to keep fighting over it anyway.

Cruz, a tea party favorite, is one of the most vocal proponents of defunding the Affordable Care Act, President Barack Obama's health care reform law. He's spent months championing the cause. But on Wednesday, as House Republican leaders unveiled their latest plan for sinking Obamacare -- tying a measure to defund the law to a must-pass resolution that keeps the government running -- Cruz thanked House Republicans for their fight, and said they're on their own.

"[Senate Majority Leader] Harry Reid will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so," Cruz said in a statement. "At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people."

Aides to top Republicans in the House, where GOP leadership has already been struggling to keep the party together on the measure, were beside themselves. And once granted anonymity, they didn't mince their words.

"We haven't even taken up the bill and Ted Cruz is admitting defeat?" fumed one senior GOP aide. "Some people came here to govern and make things better for their constituents. Ted Cruz came here to throw bombs and fundraise off of attacks on fellow Republicans. He's a joke, plain and simple."

Another aide said Cruz's comment "exposes how [Senate conservatives] have deliberately misled their constituents and the grassroots for eight weeks. This isn't leadership, it's hypocrisy."

A request for comment from Cruz's office regarding the dust-up caused by the senator's remarks was not returned.

House Republican leaders have been planning to pass their continuing resolution (with its provision to defund Obamacare) and hand it off to Cruz and others in the Senate, namely Sens. Mike Lee (R-Utah) and Marco Rubio (Fla.), to stage a dramatic fight over the issue, even if it can't pass.

The three senators issued a joint statement on Wednesday praising House Speaker John Boehner (R-Ohio) for his plan to bring the bill to the floor later this week, but none vowed to use every tool possible to carry on the fight in the Senate, such as the use of a filibuster.

House Republicans, who have spent the last few weeks being berated by Cruz on the need to keep a government shutdown on the table in the Obamacare fight, were not impressed.

"House agrees to send #CR to Senate that defunds Obamacare. @SenTedCruz & @SenMikeLee refuse to fight. Wave white flag and surrender," tweeted Rep. Sean Duffy (R-Wis.).

"So far Sen Rs are good at getting Facebook likes, and townhalls, not much else. Do something...," tweeted Rep. Tim Griffin (R-Ark.).

Rep. Tom Price (R-Ga.) also took to Twitter to vent. "House Republicans are turning words into action to defund #Obamacare. Ball will be in the Senate’s court," he wrote.

To be sure, Cruz is correct that the Democratic-led Senate doesn't have the votes to repeal Obamacare, and of course the president would never sign off on such an effort. But conservatives keep pushing votes on the issue because it's popular with their base. Cruz's statement on Wednesday was simply a tactical error: He admitted what his colleagues won't.

Not all Senate Republicans signed up for a fight over Obamacare tied to a government shutdown. Several have gone on record to oppose or criticize the strategy of pushing to defund the law in exchange for keeping the government open. Even in the House, some rank-and-file Republicans like Rep. Tom Cole (Okla.) have been vocal critics of that move.

But House Republican leaders were counting on Cruz to lead the fight in the Senate this time -- not to concede the game before it even began. Cruz's comments simply put the onus back on House Republicans to take the lead on -- and pay the political price for -- a strategy that remains unlikely to work.

Asked to respond to Cruz's statement, Boehner spokesman Michael Steel simply said, "We trust Republicans in the Senate will put up a fight worthy of the challenge that Obamacare poses."

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  • Sen. Ted Cruz (R-Texas) left, greets Former Alaska Gov. Sarah Palin (R) after introducing her at the 40th annual Conservative Political Action Conference in National Harbor, Md., Saturday, March 16, 2013. Diehard activists at the three-day conference are already picking favorites in what could be a crowded Republican presidential primary in 2016. (AP Photo/Carolyn Kaster)

  • FILE - In this Jan. 31, 2013 file photo Armed Services committee member, Republican Sen. Ted Cruz (R-Texas), questions former Sen. Chuck Hagel (R-Neb.), President Barack Obama's choice for defense secretary, during Hagel's confirmation hearing on Capitol Hill in Washington. Weeks into his job, Texas Republicans are cheering Cruz's indelicate debut and embracing him as one of their own. The insurgent Republican elected with the tea party's blessing and bankroll, has run afoul of GOP mainstays, and prompted Democrats to compare his style to McCarthyism. Also seen from left are Sen.s Roy Blunt, R-Mo., and Mike Lee, R-Utah. (AP Photo/J. Scott Applewhite, File)

  • Ted Cruz, a Republican candidate for U.S. Senate, addresses the Republican National Convention in Tampa, Fla., on Tuesday, Aug. 28, 2012. (AP Photo/Charlie Neibergall)

  • Sen. Ted Cruz (R-Texas) speaks to the media, Wednesday, Aug. 1, 2012, in Houston a day after defeating Lt. Gov. David Dewhurst in a runoff. (AP Photo/Pat Sullivan)

  • WASHINGTON, DC - MARCH 13: Sen. Ted Cruz (R-Texas) holds a news conference to announce their plan to defund the Patient Protection and Affordable Care Act, also known as Obamacare, at the U.S. Capitol March 13, 2013 in Washington, DC. Although Cruz and his fellow sponsors expect the legislation to fail, they believe it is an important survey of who supports health care reform. (Photo by Chip Somodevilla/Getty Images)

  • Sen. Ted Cruz of (R-Texas) addresses the Republican National Convention in Tampa, Fla., on Tuesday, Aug. 28, 2012. (AP Photo/J. Scott Applewhite)

  • Sen. Ted Cruz (R-Texas) answers questions from the media at a voting precinct Tuesday, July 31, 2012, in Houston. Cruz faces Lt. Gov. David Dewhurst in the Republican primary runoff election for the Republican nomination for the U.S. Senate. (AP Photo/Pat Sullivan)

  • Senator Ted Cruz (R-Texas) answers a question during an event held by the Austin Chamber of Commerce in Austin, Texas on Friday, April 5, 2013. Titled "A Conversation with Senator Ted Cruzon Business Issues," the event was held at the Four Seasons hotel and featured moderator John Holmes who asked Sen. Cruz questions from the audience. (AP Photo/Austin American-Statesman, Deborah Cannon) AUSTIN CHRONICLE OUT, COMMUNITY IMPACT OUT, MAGS OUT; NO SALES; INTERNET AND TV MUST CREDIT PHOTOGRAPHER AND STATESMAN.COM

  • Sen. Ted Cruz (R-Texas) speaks to the Spring Branch Republican Club Monday, Nov. 5, 2012, in Houston. Cruz is running against Democrat Paul Sadler to replace retiring U.S. Sen. Kay Bailey Hutchison. (AP Photo/David J. Phillip)

  • Sen. Ted Cruz (R-Texas) arrives to speak at the 40th annual Conservative Political Action Conference in National Harbor, Md., Saturday, March 16, 2013. Diehard activists at the three-day conference are already picking favorites in what could be a crowded Republican presidential primary in 2016. (AP Photo/Carolyn Kaster)

  • WASHINGTON, DC - APRIL 22: Sen. Ted Cruz (R-Texas) listens to testimony during a Senate Judiciary Committee hearing on April 22, 2013 in Washington, DC.The committee is hearing testimony on border security, economic opportunities and the Immigration Modernization Act. (Photo by Mark Wilson/Getty Images)

  • Sen. Ted Cruz (R-Texas) debates Lt. Gov. David Dewhurst, not shown, at the King Street Patriots event hall, Monday, July 23, 2012, in Houston. The two Republican candidates for the U.S. Senate have repeatedly torn into each other during the third debate as early voting began across Texas. (AP Photo/Houston Chronicle, Michael Paulsen)

  • WASHINGTON, DC - MARCH 13: Sen. Ted Cruz (R-Texas) holds a news conference to announce their plan to defund the Patient Protection and Affordable Care Act, also known as Obamacare, at the U.S. Capitol March 13, 2013 in Washington, DC. Although Cruz and his fellow sponsors expect the legislation to fail, they believe it is an important survey of who supports health care reform. (Photo by Chip Somodevilla/Getty Images)

  • Sen. Ted Cruz (R-Texas) waves as he arrives at a polling station to speak to media and voters in Dallas, Thursday, Nov. 1, 2012. Cruz faces Democratic candidate Paul Sadler for the U.S. Senate seat vacated by fellow Republican Kay Bailey Hutchison. (AP Photo/LM Otero)

  • Senator Ted Cruz (R-Texas) speaks during a news conference at the Capitol in Austin, Texas, on Monday, April 1, 2013. Cruz, along with other Republican officials, announced that they believe that Medicaid is a broken system, and that expanding it under the Affordable Care Act is the wrong move for Texas. Shown, from left, are Governor Rick Perry, US Senator John Cornyn and Lt. Gov. David Dewhurst. (AP Photo/Austin American-Statesman, Deborah Cannon)

  • WASHINGTON, DC - MARCH 22: U.S. Sen. Ted Cruz (R-Texas) talks with a reporter outside the Senate chamber on Capitol Hill March 22, 2013 in Washington, DC. The Senate voted on amendments to the budget resolution on Friday afternoon and into the evening. (Photo by Drew Angerer/Getty Images)

  • Sen. Ted Cruz (R-Texas), left, smiles as he listens to campaign chief consultant Jason Johnson go over election results as they come in Tuesday, Nov. 6, 2012, in Houston. Cruz is running against Democrat Paul Sadler to replace retiring U.S. Sen. Kay Bailey Hutchison. (AP Photo/David J. Phillip)