WASHINGTON (AP) — Grasping for a deal on the nation’s debt, President Barack Obama and congressional leaders remained divided Sunday over the size and the components of a plan to reduce long term deficits. Noting the need to work out an agreement over the next 10 days, the president and lawmakers agreed to meet again Monday.

Obama also sought to use the power of his office to sway public opinion, scheduling a news conference for Monday morning, his second one in less than two weeks devoted primarily to the debt talks.

Officials familiar with the meeting said Obama pressed the eight House and Senate leaders Sunday evening to continue aiming for a massive $4 trillion deal for reducing the debt. He especially objected to Republican claims that there was not enough time to negotiate a deal that large, two officials said.

But there appeared to be little appetite for such an ambitious plan and the political price it would require to pass in Congress. Instead, House Speaker John Boehner told the group that a smaller package of about $2 trillion to $2.4 trillion was more realistic.

Officials spoke on the condition of anonymity to describe the private meeting and because of the sensitivity of the negotiations.

One Democratic aide said Obama and Sen. Jon Kyl, the second-ranking Republican leader in the Senate, exchanged some testy words after Obama objected to the way Republicans were negotiating.

A Democratic official familiar with the session said House Majority Leader Eric Cantor, R-Va., was especially adamant that any deficit reduction package could not contain tax increases and that any new tax revenue would have to be used to pay for other tax benefits.

Obama and the congressional leaders met in the Cabinet Room of the White House for the rare Sunday session. Most appeared in casual Sunday clothes, with open-collared shirts underneath blazers.

When a reporter asked, “Can you work it out in 10 days, sir?” Obama replied, “We need to.”

Time is becoming increasing precious in the negotiations. The deficit reduction talks are linked to the government’s need to increase its borrowing limit, now capped at $14.3 trillion. The Obama administration says if the debt ceiling is not raised by Aug. 2, the nation would default on its obligations, with potentially calamitous financial consequences worldwide.

Officials said Obama time and again pressed for a larger package. He also pointed out that the smaller deal of up to $2.4 trillion still would require tax revenues and that not all of the details had yet been worked out.

Participants appeared to spend a significant amount of time debating whether a bipartisan group, led by Vice President Joe Biden, had actually identified $2.4 trillion in deficit reduction. Obama cautioned the room that the actual number was smaller and would require additional measures.

One Republican briefed about the meeting said Biden pointed out that that package also would require tax revenue and urged Boehner to back away from his formula that every dollar increase in the debt limit should equal the amount of deficit reduction. Obama wants the debt ceiling raised through the end of 2012, to avoid having to raise it again during the presidential elections. That would require about a $2.4 trillion increase, and thus, a $2.4 trillion deficit reduction over 10 years.

Boehner would not budge from his formula, however, the Republican officials said.

Attending the meeting were Boehner, Cantor, House Democratic leader Nancy Pelosi and her second in command, Steny Hoyer of Maryland. Representing the Senate were Democratic leader Harry Reid of Nevada and party whip Richard Durbin of Illinois, and Republican leader Mitch McConnell of Kentucky and Kyl, his top lieutenant.

Reid spokesman Adam Jentleson said Reid supported a “robust” package.

“Senator Reid believes the stakes are too high for Republicans to keep taking the easy way out, and he is committed to meeting every day until we forge a deal, however long that takes.” Jentleson said.

McConnell spokesman Don Stewart chided Democrats and the president for continuing to pursue additional tax revenue.

“It’s baffling that the president and his party continue to insist on massive tax hikes in the middle of a jobs crisis while refusing to take significant action on spending reductions at a time of record deficits,” McConnell spokesman Don Stewart said.

Earlier, White House Chief of Staff Bill Daley said in a television interview that Obama would not “walk away from a tough fight.”

“Everyone agrees that a number around $4 trillion is the number that will … make a serious dent in our deficit,” he said.

But embedded among the tough words was rhetoric that acknowledged the prospects for the “big deal” had become uncertain at best.

“We’re going to try to get the biggest deal possible,” said Treasury Secretary Timothy Geithner.

Earlier Sunday, McConnell left little doubt that the $4 trillion deal was dead.

“I think it is,” McConnell said. Raising taxes amid 9.2 percent unemployment, he added, “is a terrible idea. It’s a job killer.”

The discussions were attracting attention overseas.

The International Monetary Fund’s new chief, Christine Lagarde, said that if the U.S. fails to raise its debt limit, she foresees “interest hikes, stock markets taking a huge hit and real nasty consequences” for the American and global economies.

“I would hope that there is enough bipartisan intelligence and understanding of the challenge that is ahead of the United States, but also the rest of the world,” she said.

While Republicans have fought against higher taxes, Obama also has a long way to go to satisfy lawmakers in his own party. Many Democrats are unnerved by the president’s $4 trillion proposal because of its changes to Medicare and Medicaid.

Political pain is part of the deal and should be worth bearing, Daley said. Obama, he added, was calling on lawmakers to “step up and be leaders.”

The package of $2 trillion to $2.4 trillion in deficit reduction identified by the Biden-led negotiators would still require Republicans to accept some increase in tax revenue. Republicans walked out of those negotiations after they were unable to accept about $400 billion in new tax money that the White House proposed by closing loopholes, ending some corporate subsidies, and limiting the value of deductions for wealthy taxpayers.

One option now under consideration by Obama administration officials would call for capping some deductions for wealthy taxpayers at the 28 percent tax rate and using the revenue to help pay for a yearlong extension of a current payroll tax cut. The extension would expire at the end of 2012, but the cap on deductions would continue, generating new revenue in the long term. Capping all itemized deductions at the 28 percent rate would generate about $293 billion over 10 years.

Republicans have said they are not interested in such a bargain.

Daley was on ABC’s “This Week,” as was Lagarde. McConnell appeared on “Fox News Sunday” and Geithner was interviewed on NBC’s “Meet the Press” and CBS’ “Face the Nation.”

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Associated Press writer Andrew Taylor contributed to this report.