Income tax rates are set to increase across the board with the start of 2013, although lawmakers and President Barack Obama still hope to enact a rollback before the 112th Congress ends Thursday.

Senate Democrats emerged from a caucus Monday night saying they expected a strong vote in support of a bargain struck earlier between the White House and Senate Republicans.

Some Democrats expressed initial concerns about the terms of the agreement, while Republicans appeared more inclined to support it. But several Democrats said that the compromise, despite its shortcomings, was preferable to sending the nation over the fiscal cliff.

“The disagreements on this provision, that provision another provision are far and wide,” said Charles E. Schumer, D-N.Y. “But the number of people who think we should go over the cliff rather than vote for this is very small.”

Several Democrats said they were assured that Obama will not agree to additional spending cuts as part of a bargain with Republicans when a debt ceiling increase is needed in the next couple of months.

Majority Leader Harry Reid, D-Nev., said he was awaiting a Congressional Budget Office scoring before bringing the agreement to the Senate floor in the early hours of New Year’s Day.

But when the House adjourned Monday evening until noon Tuesday, that ended any hope that the tax increases would be blocked before the midnight expiration of tax rates first set in 2001 and 2003. The timing could be politically fortuitous for House members. Since tax rates increase when the new year begins, the House could find itself considering a measure that amounts to a huge tax cut.

Vice President Joseph R. Biden Jr., who played a central role after being drawn into the talks Sunday evening by Senate Minority Leader Mitch McConnell, R-Ky., met with Democratic senators Monday night.

Senate Finance Chairman Max Baucus, D-Mont., declined to say whether he liked the deal, but added, “it’s an agreement and that’s good.”

The House adjourned after waiting all day for the Senate to complete a bipartisan agreement that would limit the tax increases to upper-income taxpayers and delay automatic spending cuts scheduled to begin Wednesday. Speaker John A. Boehner, R-Ohio, has said the House will not act to address the fiscal cliff unless and until it receives Senate-passed legislation.

Sources said the negotiators settled on a $450,000 earnings threshold for extending existing tax rates. The final hurdles appeared to be how to cover the $24 billion cost of delaying the spending cuts by two months, and whether the estate tax exemption should be adjusted for inflation.

On Monday afternoon, McConnell suggested that Congress move ahead with tax legislation and put off dealing with the sequester. “We have reached agreement on all of the tax issues,” McConnell, R-Ky., told the Senate. “Let’s take what has been agreed to and get moving.”

McConnell spoke shortly after Obama, in a pep-rally-style appearance that irritated Republicans, said a deal is “within sight” and claimed victory in his bid to make upper-bracket taxpayers pay more.

But talks continued well into the evening. Republican senators and aides said the two sides had agreed to almost every provision in a deal when Democrats pushed Monday morning for a short-term delay in the sequester that would be offset with new tax revenue or unspecified spending cuts in 2015.

Negotiators agreed to renew extended unemployment compensation benefits for a year without offsetting the cost. Offsets were being discussed for the cost of calling off scheduled cuts in Medicare payments to health care providers.

Bob Corker, R-Tenn., said McConnell called for passage of a more limited deal “because of the position they [Democrats] have been taking all day — it’s the issue of deciding that, instead of substituting other [spending] reductions for the sequester, you’re going to substitute revenues for it. That is like a 180-degree reversal from where we’ve been on that issue.”

A GOP aide said Republicans offered $100 billion in spending cuts that could be used to offset the sequester delay, saying those were similar to cuts that have been used as offsets in the past. “So far they’ve rejected all of those,” he said. “Given that this was a late ask, after we already had a deal, there’s some significant doubt about whether Democrats want a deal.”

Tentative Deal on Taxes

Sources familiar with the negotiations said the agreement on taxes would split the difference between recent proposals by the two parties, extending current tax rates for individuals’ income up to $400,000 and couples’ income up to $450,000.

Tax rates on capital gains and dividends would increase from 15 percent to 20 percent for those above those income thresholds, while personal exemption and itemized deduction phase-outs would be reinstated for families earning more than $250,000.

Although negotiators have had trouble reaching an accord on the estate tax, they appeared to compromise at taxing estates worth more than $5.12 million at a top rate of 40 percent. Democrats wanted to set the estate tax rate at 45 percent, while Republicans sought continuation of the current 35 percent top rate.

As news of the framework for an agreement spread on Monday, there appeared to be anxiety among liberals that the White House had conceded too much in setting the new rate thresholds.

Tom Harkin, D-Iowa, described the emerging framework as “grossly unfair” because, he said, it would include permanent tax policies but only a temporary extension of unemployment benefits and overall not do enough to assist low and middle-income earners. “If we’re going to have some kind of a deal, the deal must be one that really does favor the middle class, the real middle class, those that are making $50,000, $60,000, $70,000 a year,” he said.

However, Barbara Boxer, D-Calif., called an apparent decision to renew extended unemployment benefits, “very, very important.”

Sam Goldfarb and Paul M. Krawzak contributed to this report.