Federal debt talks remained at a stalemate Thursday as both sides continued their week-long battle of blaming each other for the stymied negotiations to allow the Treasury to continue borrowing money to finance government operations.

Even as senior officials suggested that a deal needed to be reached by July 22, allowing 11 or 12 additional days for legislative action, both sides engaged in showmanship.

Senate Majority Leader Harry M. Reid (D-Nev.) canceled his chamber’s planned week-long Fourth of July break, calling all senators back to Washington next week even though there is no major legislation ready for consideration. Minutes later, Senate Minority Leader Mitch McConnell (R-Ky.) took to the floor to offer a last-minute invitation to President Obama to meet with Senate Republicans to discuss the issue, fully aware that the president didn’t have the time on his schedule.

“I’d like to invite the president to come to the Capitol today to join Republicans for lunch, or at any time this afternoon that he can make it. That way he can hear directly from Republicans why what he’s proposing won’t pass. And we can start talking about what’s actually possible,” McConnell said.

Nearly two months into serious negotiations, Obama and congressional leaders are trying to secure more than $2 trillion in budget savings as part of legislation that would increase the debt ceiling by a similar amount. The current ceiling of $14.3 trillion has already been breached, and Treasury Secretary Timothy F. Geithner has said he has until Aug. 2 to maneuver federal accounts to avoid defaulting on outstanding debts.

Democratic officials familiar with the talks said the negotiations have moved into a new phase, in which party leaders must decide what their troops can support. They expressed optimism that a deal is still within reach to trim at least $2 trillion from projected borrowing over the next decade. Those officials said Congress could meet the Aug. 2 deadline if consensus is forged by July 22.

That would allow enough time to draft the actual legislation, allow the Congressional Budget Office time to formally assess its fiscal impact and then have the House and Senate approve what is certain to be a complex mix of measures.

This makes the next three weeks of talks critical. If no framework for a pact is reached by then, Congress will have to approve a short-term increase in the debt ceiling — something almost all leaders have objected to doing — or risk a collapse in financial markets in early August as the final pieces of a debt deal are put into place.

The two sides continued jousting most acutely over the Democratic position that more than $400 billion in increased tax revenue should be part of the talks, money that would come from closing some corporate loopholes and limiting deductions.

The early phase of negotiations, between Vice President Biden and six congressional leaders, hammered out about $1 trillion in agreed-to spending cuts, with a few hundred billion dollars more in savings that were close to agreement. Advisers in both parties have said there is still a shortfall to clear $2 trillion in savings, which has prompted the fight over whether to seek increased revenue through tweaking the tax code.

Senators were to spend the Fourth of July holiday week in their home states, but Reid talked to Obama about the political appearance of such a break, according to a Senate aide. Then, on Wednesday, Obama used a news conference to challenge lawmakers to stay in town to work on a debt-reduction package.

“It is often said that with liberty comes responsibility. We should take that responsibility seriously. I’m confident we do. That’s why the Senate will reconvene Tuesday, the day after the Fourth,” Reid said Thursday. “We’ll do that because we have work to do.”

With no bipartisan talks on anyone’s schedule, Reid invited Obama and Biden to meet with the entire Senate Democratic caucus Wednesday. A similar meeting with the White House economic team is planned for Thursday.

At his press conference, Obama had scolded lawmakers for stalling the negotiations when time is running out. “You need to be here,” he said. “I’ve been here.”

Staff writers Lori Montgomery and Felicia Sonmez contributed to this report.