WASHINGTON — Furious negotiations between the White House and the Senate Republican leadership Monday got Washington close to a fiscal cliff resolution, but nothing was going to pass in time for the House and Senate to meet their Dec. 31 deadline for averting automatic tax increases and spending cuts deemed a threat to the economy.

Some senators pushed for a quick vote on legislation, but the House wasn’t going to consider any deal until Tuesday at the earliest, meaning that those increases and cuts would go into effect for the first days of 2013. If Congress acts quickly and sends a deal to President Barack Obama, the economic effect would be very limited.

There was word Monday night that a late New Year’s Eve vote to ratify the deal was possible in the Senate, barring opposition from majority Democrats. Vice President Joe Biden was headed to the Capitol to brief the Democratic rank and file.

Under the agreement, tax rates would jump to 39.6 percent from 35 percent for individual incomes more than $400,000 and couples more than $450,000, and tax deductions and credits would start phasing out on incomes as much as $250,000.

In a development that pushed lawmakers closer to a resolution, Senate Republicans said negotiators agreed to put off $110 billion in across-the-board cuts to military and domestic programs for two months while broader deficit reduction talks continue. Those cuts begin to go into force Wednesday.

The nature of the deal ensures that the running war between the White House and congressional Republicans on spending and taxes will continue at least until the spring. Treasury Secretary Timothy F. Geithner formally notified Congress that the government reached its statutory borrowing limit on New Year’s Eve. Through some creative accounting tricks, the Treasury Department can put off action for perhaps two months, but Congress must act to keep the government from defaulting just when the “pause” on pending cuts is up. Then in late March, a temporary law financing the government expires.

And the new deal does nothing to address the big issues that Obama and Speaker John Boehner hoped to deal with in their failed “grand bargain” talks two weeks ago: booming entitlement spending and a tax code so complex that few defend it anymore.

Although the tentative deal has a chance of success, it first landed with a thud on Capitol Hill. Republicans accused the White House of “moving the goal posts” by demanding still more tax increases to help shut off across-the-board spending cuts beyond the two-month pause.

Democrats were incredulous that the president had ultimately agreed to around $600 billion in new tax revenue over 10 years when even Boehner had promised $800 billion. But the White House said it had won concessions on extended unemployment insurance and the inheritance tax.

“No deal is the worst deal,” said Sen. Joseph I. Lieberman, I-Conn., rejecting the assertions of liberal colleagues that no deal would be better than what they would see as a bad deal.

Even after dark, however, new wrenches were gumming up the machinery. Democrats put out late word that Republicans wanted the threshold at which estates would be taxed to be indexed to inflation, a nonstarter for them. Republicans said they needed to see what cuts would pay for the $24 billion needed to put off across-the-board spending cuts.

But with Republicans and Democrats grumbling, it was clear that a deal hashed out through intense talks between Joe Biden and Sen. Mitch McConnell of Kentucky, the Republican leader, had given both sides provisions to cheer and to jeer.

President Obama said an agreement was “within sight” but “not done,” showing the continuing uncertainty.

An official familiar with the negotiations stressed that taxes would rise in some sense on the top 2 percent of earners, as Obama has wanted since his first presidential campaign in 2008. That is because the deal would reinstate provisions to tax law, ended by the Bush tax cuts of 2001, that phase out personal exemptions and deductions for the affluent.