Washington ? 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 today.

Obama also sought to use the power of his office to sway public opinion, scheduling a news conference for this 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.

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.

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 familiar with the meeting spoke on the condition of anonymity because of the delicate nature of the negotiations. 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.

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.

It was an abrupt change from 24 hours earlier. Republicans late Saturday rejected the $4 trillion proposal, the largest of three under consideration, because its tax increases would doom it in the GOP-led House, Speaker John Boehner said.

The Ohio Republican informed Obama that a package of about $2 trillion, which bipartisan negotiators had identified but not agreed to, was more realistic.

Senate GOP leader Mitch McConnell of Kentucky 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 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.