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But both sides are also under enormous pressure to resist each other’s demands. On Tuesday, Mr. Obama met with liberal leaders at the White House and they urged him to reject any deal that would cut Social Security or Medicare.

“The truth is America does not face an ‘entitlement crisis.’ We should not be cutting Social Security and Medicare benefits to put our fiscal house in order,” said Max Richtman, president of the National Committee to Protect Social Security & Medicare.

The so-called fiscal cliff hits early next year. The Bush-era tax cuts expire Jan. 1, and $110 billion in automatic spending cuts take effect Jan. 2 as a result of last year’s debt deal. The tax increases would apply across the board, while the spending cuts would be divided equally between defense and domestic appropriations.

Together, they would plunge the economy into a short but sharp recession — though the tax increases and spending cuts also would reduce the budget deficit dramatically in 2013, and would produce a stronger economy by the end of the decade, according to the Congressional Budget Office.

Some Democrats have suggested that their party should let the fiscal cliff hit and then negotiate from a position of strength when Democrats get additional members early next year. They gained seats last week in both chambers, though they will hold a majority only in the Senate.

But House Minority Leader Nancy Pelosi, California Democrat, flatly rejected that Tuesday.

“I want you to be disabused of any notion that there’s any widespread thought that it would be a good thing for our country for us to go over the cliff,” she told reporters.

Getting there, however, will take a deal — which has been elusive for the past 18 months.

Mr. Obama has invited congressional leaders to the White House on Friday to start negotiations anew.

But signs of calcification already are setting in.

In one ominous sign, the Senate picked up right where it left off in September, fighting over a bill to open more federal lands to fishing and hunting.

Mr. Reid used procedural tactics to lock out Republican amendments, saying the GOP is threatening to delay the bill, as it did with many of Democrats’ priorities over the past two years.

“I can’t imagine why we’re still fighting the battles of the last election,” he said.

But Republicans say Mr. Reid is pushing a partisan agenda and in restricting amendments he is refusing to allow the freewheeling debate the Senate usually enjoys.