White House asks GOP to go for the 'holy grail' in deficit package

With deficit-reduction talks mired in tension and division, the White House's top spokesman challenged Republicans Thursday to go for the “holy grail" and push for the biggest deal possible.

White House press secretary Jay Carney said that despite reports of heated exchanges in Wednesday afternoon's meeting between congressional negotiators, the president would on Thursday continue to ask Republicans to do something "generational."

"That agreement is right here," Carney said. "It's on the table. You just have to be willing to reach for it."

Carney repeatedly challenged Republicans during the daily press briefing to lead and not posture for "narrow constituencies within your own party."

Despite White House optimism that the parties are inching closer to a deal, the clock is ticking closer to the Aug. 2 deadline set by the Treasury Department for raising the debt ceiling.

House Republicans claimed debt-ceiling negotiations at the White House ended in acrimony Wednesday when President Obama warned House Majority Leader Eric CantorEric Ivan CantorFeehery: The governing party 'Release the memo' — let's stop pretending that Democrats are the defenders of the FBI Raúl Labrador, a model for Hispanic politicians reaching higher MORE (R-Va.) not to call his bluff about rejecting a short-term increase in the debt ceiling. Cantor said Obama then “abruptly” walked out of the meeting.

A Democratic source said the reports of a dramatic walk-out by Obama were overblown, but the source acknowledged that once the president “said what he was going to say, he got up and walked out.”

Despite the tensions, Carney said that the "holy grail" of think tanks, good government groups and members of both parties is within reach if leaders will compromise and seize the opportunity to rein in the deficit.

Lawmakers are scheduled to reconvene at 4:15 p.m. at the White House to continue the talks. Carney acknowledged that he is "not expecting today a Hallelujah moment" in the negotiations.

Carney also refused to join Senate Majority Leader Harry ReidHarry Mason ReidWATCH: There is no Trump-Russia collusion and the media should stop pushing this The demise of debate in Congress ‘North by Northwest,’ the Carter Page remake MORE (D-Nev.) and Sen. Charles SchumerCharles (Chuck) Ellis SchumerDemocrats now attack internet rules they once embraced Schumer: Trump budget would ‘cripple’ gun background checks Schumer: Senate Republicans' silence 'deafening' on guns, Russia MORE (D-N.Y.) in calling for Cantor to be kicked out of the talks.

"The president believes that we have to reach a deal with the leaders of Congress of both parties," Carney said. "What's important is that everybody decides to play the role of leader."