Updated: 10:26 p.m.

President Barack Obama and Congressional leaders continued to slog through debt limit negotiations at the White House on Tuesday with no clear resolution in sight, according to several Hill sources familiar with the meeting.

While Senate Minority Leader Mitch McConnell (R-Ky.) presented his emergency fallback proposal to raise the debt limit, which attempts to shift most of the political burden onto the president, the focus of the negotiators was still to get a real deal, the Hill sources said.

Speaker John Boehner (R-Ohio) “urged the president to show leadership and again asked that he present a score-able plan of his own that could pass the Congress,” a Republican familiar with the talks said.

Boehner also urged the president and Democratic leaders to work with the GOP to pass a balanced budget amendment to the Constitution, which Democrats roundly dismiss.

At one point, according to Democratic sources, House Majority Leader Eric Cantor (R-Va.) asked Obama to detail his own proposals, and the president said he gave them to Boehner and he has to assume that if he’s speaking to Boehner, he’s speaking to the entire House GOP Conference.

Cantor spokesman Brad Dayspring disputed that statement. “We are told that the President is incorrect and there have been no details of the President’s preferred plan put on paper, and the Majority Leader is again requesting that those details be released so that we can share them with our Members,” Dayspring said in an email.

Boehner told Fox News after the meeting that he had yet to see an entire plan from the president.

“I think the big issue for today was — Mr. Cantor and I, the Majority Leader in the House — really pressed the president for, you know, where’s his plan?” Boehner said. “We’ve talked about a lot of possibilities. He and I had conversations for a couple weeks. But we’ve never really seen the whole plan and what they’re really willing to do. … They had some ideas, but they never would quite put them on paper.”

The Democratic sources said Cantor also complained about leaks from the previous meeting about his Medicare proposal and how it was portrayed.

White House Press Secretary Jay Carney, meanwhile, praised McConnell’s proposal, saying it reaffirmed “what leaders of both parties have stated clearly, that defaulting on America’s past due bills is not an option.”

But the president still wants a bigger deal, and he warned during an interview with “CBS Evening News” on Tuesday that Social Security and other payments to the public may be interrupted if the nation’s debt ceiling is not raised by Aug. 2.

“The president continues to believe that our focus must remain on seizing this unique opportunity to come to agreement on significant, balanced deficit reduction,” Carney said. “As the president has said, ‘If not now, when?’”

Democrats at Tuesday’s meeting pushed back against the GOP contention that the debt limit is Obama’s problem, according to another Democratic source. House Majority Whip Steny Hoyer (D-Md.) said they all own the issue, and he continued to urge a comprehensive deal, the source said.

The talks are expected to continue daily until a resolution is reached. The next meeting will be held at 4 p.m. Wednesday at the White House.