WASHINGTON -- Senate Minority Leader Mitch McConnell (R-Ky.) said Tuesday that the nation's debt limit won't be raised unless Republicans can extract concessions from Democrats and President Barack Obama.

The borrowing limit, which was suspended until Feb. 7, 2014, as part of the deal to end the government shutdown in the fall, stands at about $17.2 trillion. The Treasury Department estimates that without a hike, it can keep paying the nation's bills only until sometime in March.

The budget agreement that passed the House overwhelmingly last week and is set for passage in the Senate -- likely on Wednesday -- would also require a boost in the debt ceiling in order to carry out the spending that it mandates. But McConnell said Republicans would not allow that.

"I doubt if the House or, for that matter, the Senate is willing to give the president a clean debt ceiling increase," McConnell told reporters on Capitol Hill. "Every time the president asks us to raise the debt ceiling is a good time to try to achieve something important for the country."

He added that holding the borrowing cap hostage is the only way the GOP can get Obama to negotiate.

"I think the debt ceiling legislation is a time that brings us all together and gets the president's attention, which with this president, particularly when it comes to reducing spending, has been a bit of a challenge," McConnell said.

He did not lay out what demands the GOP would make. "We'll have to see what the House insists on adding to it as a condition of passage," McConnell said.

House Budget Committee Chairman Paul Ryan (R-Wis.) made similar remarks on Sunday, saying, "We don’t want nothing out of this debt limit."

For his part, Senate Majority Leader Harry Reid (D-Nev.) said he didn't see Republicans being up for another damaging showdown over something that's essential to keeping the government and economy moving after they were so battered over the October shutdown.

"I can't imagine the Republicans want another fight on debt ceiling," Reid told reporters. "We've passed two debt ceilings in the very recent past, and we should do another one."

Still, Republican lawmakers are taking criticism from right-wing groups over the current budget deal, and those same groups oppose hiking the debt limit. House Speaker John Boehner (R-Ohio) suggested last week that such organizations would no longer have much influence in Congress, but they have sway with GOP lawmakers facing primaries next year, such as McConnell.

Michael McAuliff covers Congress and politics for The Huffington Post. Talk to him on Facebook.

Also on HuffPost:

Loading Slideshow...
  • We Mean It... Smile!

    It's not often we see Sen. Mitch McConnell (R-Ky.) crack a smile. He dons his go-to straight face most of the time. Ahead, see the rare grins of the Kentucky senator. (Photo by T.J. Kirkpatrick/Getty Images)

  • McConnell Cracks A CPAC Smile

    McConnell waves as he arrives to speak at the 40th annual Conservative Political Action Conference in National Harbor, Md. (AP Photo/Manuel Balce Ceneta, File)

  • Happy To Hang With Obama

    President Barack Obama is greeted by McConnell as he arrives at the U.S. Captiol for his third day of meetings with members of Congress March 14, 2013. (Chip Somodevilla/Getty Images)

  • Leaving The Senate, McConnell Smirks

    McConnell leaves the Senate chamber to caucus in the US Capitol Dec. 30, 2012. (Molly Riley/AFP/Getty Images)

  • Smiley Senate Exit

    McConnell leaves his office and walks toward the Senate floor on Capitol Hill March 22, 2013. (Drew Angerer/Getty Images)

  • Ready For His Close Up

    McConnell tours the stage during preparations at the Tampa Bay Times Forum Aug 26, 2012. (BRENDAN SMIALOWSKI/AFP/GettyImages)

  • A Smile And A Hug

    McConnell greets US President Barack Obama following Obama's address to a Joint Session of Congress about the US economy and job creation Sept. 8, 2011. (SAUL LOEB/AFP/Getty Images)

  • McConnell Happily Takes To The Podium

    McConnell smiles as he speaks to the press with fellow Republican senators John Barroso of Wyoming and John Cornyn of Texas at the Capitol Aug. 2, 2011. (NICHOLAS KAMM/AFP/Getty Images)

  • Thumbs Up!

    McConnell gives the the thumbs-up as he walks to the Senate floor after a deal was reached to avert a US default at the Capitol in Washington July 31, 2011. (NICHOLAS KAMM/AFP/Getty Images)

  • Sworn In And Smiling

    McConnell is sworn in by Vice President Dick Cheney as his wife Labor Secretary Elaine Chao holds the Bible during a swearing in reenactment ceremony at the US Capitol Jan. 6, 2009. (KAREN BLEIER/AFP/Getty Images)

  • Smiling On Stage At RNC

    McConnell smiles during sound check at the Republican National Convention (RNC) in Tampa, Fla., Aug 27, 2012. (Scott Eells/Bloomberg via Getty)

  • Something's Funny!

    McConnell laughs with Louisville Mayor Jerry Abramson at the annual ham breakfast at the Kentucky State Fair in Louisville, Ky., in 2010. (AP Photo/Ed Reinke)

  • McConnell Laughs Some More

    Sen. Lamar Alexander (R-Tenn.) jokes with reporters as McConnell, laughs in the Ohio Clock Corridor following the Senate Republicans' policy lunch in June 21, 2011. (Photo By Bill Clark/Roll Call)

  • Lots Of Laughing

    Sen. Roy Blunt (R-Mo.), McConnell, and Sen. Marco Rubio (R-Fla.), share a laugh during news conference in the Capitol after a meeting of Senate Republicans, Feb. 8, 2012. (Photo By Tom Williams/CQ Roll Call)