WASHINGTON — With pressure continuing to build but no breakthroughs in sight, budget bargaining between President Barack Obama and top lawmakers resumes today at the White House, with both sides hoping to slash the deficit as the price for permitting the government to borrow more than $2 trillion to pay its bills.

In a rare Sunday meeting in the White House Cabinet Room, Obama continued to push for a “grand bargain” in the range of $4 trillion worth of deficit cuts over the coming decade, but momentum is clearly on the side of a smaller measure of perhaps half that size. Obama continues to press for revenue increases as part of any agreement but Republicans remain stoutly opposed — despite some private hints to the contrary last week by House Speaker John Boehner, R-Ohio.

Obama was scheduled to hold a news conference this morning. The third White House meeting since Thursday is slated for the afternoon.

An Aug. 2 deadline looms to stave off a potentially disastrous first default on U.S. obligations, but the two sides seem no closer than they were when Republicans withdrew from talks led by Vice President Joe Biden more than two weeks ago, citing an impasse on taxes.

Last week, Boehner and Obama had private talks that led Democrats to believe the House speaker was willing to entertain revenue increases as part of a full overhaul of the tax code later this year in exchange for Democrats agreeing to stiff curbs on the growth of Medicare and lower increases in Social Security cost-of-living adjustments. But Boehner recoiled and abandoned the idea Saturday night in a move that rattled the talks.

Sunday’s sometimes testy session was shorter than some had anticipated and it’s clear neither side is willing to budge on taxes. Democrats say tax increases are a prerequisite for big spending cuts; Republicans rule out the idea unless taxes are lowered elsewhere.

“The sides are at loggerheads,” Rep. Chris Van Hollen of Maryland, the top-ranking Democrat on the House Budget Committee, said in a nationally broadcast interview this morning.

Today’s meeting will feature a discussion of tentative agreements reached in the discussions led by Biden. They include cuts to farm subsidies, student aid, federal workers’ pensions and domestic agency budgets, among others.

Van Hollen blamed Republicans, saying “they refuse to eliminate any of these tax breaks for corporate special interests — corporate jets, oil and gas companies and folks at the very high end of the income scale.”

South Carolina’s Sen. Jim DeMint, a Republican, argued that Obama “still has not given us a proposal we can accept or reject.”

“We’re not going to default. We’ve got the money. We don’t need to panic,” DeMint said.

Republicans say the Biden group identified more than $2 trillion in cuts, but Democrats put the true figure significantly lower — in large part because many of their concessions on spending cuts relied on the assumption Republicans would accept some new tax revenues. But the Biden group was bitterly divided over taxes, as Republicans like House Majority Leader Eric Cantor of Virginia repulsed Democratic demands to shut down tax breaks for oil and gas companies and deductions enjoyed by the wealthy. And Republicans resisted Democratic attempts for a mechanism to guarantee the Pentagon would contribute to cuts.

“The Speaker told the group that he believes a package based on the work of the Biden group is the most viable option at this time for moving forward,” said a Boehner spokesman.

Sunday’s meeting featured some tense exchanges, officials briefed on the talks said, as Democrats accused Republicans of being inflexible. And officials briefed on the talks said Obama sharply rebuked Republicans for saying there’s no time for a “grand bargain” blending new revenues with big spending cuts — including curbs to Social Security and Medicare.

“If not now, when?” Obama asked, according to a Democratic official requiring anonymity because the session was private.

Senate GOP Leader Mitch McConnell, R-Ky., said a big $4 trillion bargain is off the table.

“Everything they told me and (Boehner) is that to get a big package would require a big tax increase in the middle of an economic situation that’s extraordinarily difficult, with 9.2 percent unemployment,” McConnell said on “Fox News Sunday.” “We think it’s a terrible idea. It’s a job-killer.”