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But the bigger problems loom with the “fiscal cliff.”

Unless Congress takes action, the George W. Bush-era tax cuts are slated to expire Jan. 1, and a day later $110 billion in automatic spending cuts — the result of last year’s debt deal — also will take effect.

Together, they would plunge the U.S. into a short but deep double-dip recession — though they also would leave the federal budget in much better shape and would produce a stronger economy by the end of the decade, according to the Congressional Budget Office.

Both sides in Congress, though, say the tax increases and spending cuts are simply too much to stomach right now.

Democrats on Tuesday expanded their majority to at least 54-45 in the Senate, with one senator, Maine independent Angus King, not saying with which party he will caucus. In the House, the Republican majority dropped, though 10 seats were still to be decided as of Wednesday evening.

In the race for the White House, Mr. Obama’s 2008 margins dropped in the popular vote and the Electoral College — and Florida was still too close to call Wednesday. But even without Florida, Mr. Obama has won another four years in office to try to fulfill his election promises.

Mr. Boehner said any deal with Mr. Obama must have the White House agree to lower spending on entitlement programs such as Medicare and Medicaid, which take up an ever-increasing share of government spending.

Grover Norquist, head of Americans for Tax Reform, which sponsors an influential no-new-taxes pledge to which many Republicans are beholden, said the revenue deal Mr. Boehner is offering passes muster.

“I heard the speaker say again and again, let’s not raise taxes, let’s have economic growth,” Mr. Norquist told The Washington Times. He said raising growth to 4 percent a year, up from the 2 percent that he said Mr. Obama has struggled to hit, would mean an additional $5 trillion in tax revenue over 10 years.

He said that comes without raising tax rates, but still would give Mr. Obama solid revenue numbers to point to — though it’s unlikely the CBO, which keeps official score of legislation, would calculate it that way.

“We’re trying to get the president to actually put something down in writing and to engage in governing So let’s take it a step at a time. This is new to him,” Mr. Norquist said.

Mr. Obama ran for re-election on a call to raise income tax rates on Americans with the highest incomes, while holding rates low for everyone else. Republicans, though, said raising taxes on the wealthy amounted to a tax increase on small businesses.

Mr. Boehner pointed back to discussions he had with Mr. Obama last year, during the height of the debt showdown, when he said they talked about a deal that would lower tax rates but close enough loopholes to bring in more money into federal accounts.