With some Congressional Democrats fretting that the administration would give in too easily, senior White House officials said Mr. Obama was insisting on the jobless aid and the extension of other tax breaks for middle- and lower-income Americans included in the 2009 stimulus plan as a condition of any deal. Republicans said they were considering those demands.

Many other taxes, including the estate tax, the alternative minimum tax and taxes on capital gains, interest and dividends, were also part of the talks.

The formal negotiations were being conducted by senior lawmakers from both parties, along with the Treasury secretary, Timothy F. Geithner, and the White House budget director, Jacob Lew. But there were also direct talks under way between the West Wing and Republicans, including the Senate minority leader, Mitch McConnell of Kentucky.

Mr. McConnell accused Democrats of holding show votes for political reasons but said he was optimistic that a solution would be reached before Congress adjourns. “I am relatively confident that the end of this process will lead us into, I think, a very sensible decision not to raise taxes on anybody in the middle of a recession,” he said.

The majority leader, Harry Reid of Nevada, said he was hopeful an agreement would be reached by Wednesday, allowing the Senate to move forward with a busy end-of-year agenda.

But some Senate Democrats were growing increasingly angry at the administration and wary of a deal. In a sign of the deepening divisions, White House officials had voiced opposition to raising the threshold for the tax breaks to $1 million, saying it would do little to reduce the deficit.

The rejection of that proposal underscored a harsh defeat for Democrats in both the policy debate and on the political messaging front. Some of them lashed out at Republicans in response, accusing them of holding tax cuts for the middle class “hostage” to secure tax breaks for the wealthy.