WASHINGTON — Senate leaders neared the completion Monday night of a bipartisan deal to raise the debt ceiling and end the government shutdown while the rest of the world braced for the possibility of an American default that could set off a global financial disaster.

Negotiators talked into the evening as senators from both parties coalesced around a plan that would lift the debt limit through Feb. 7, pass a resolution to finance the government through Jan. 15 and conclude formal discussions on a long-term tax and spending plan no later than Dec. 13, according to one Senate aide briefed on the plan.

But while both Senator Mitch McConnell of Kentucky, the Republican leader, and Senator Harry Reid of Nevada, the Democratic leader, praised the progress that was made in the Senate, it was already clear that the most conservative members of the House were not going to go along quietly with a plan that does not accomplish their goal from the outset of this two-week-old crisis: dismantling the president’s health care law.

“We’ve got a name for it in the House: it’s called the Senate surrender caucus,” said Representative Tim Huelskamp, Republican of Kansas. “Anybody who would vote for that in the House as Republican would virtually guarantee a primary challenger.”