Mr. McConnell, interviewed on the NBC television program “Meet the Press,” flatly confirmed the outlines of that compromise. “I think we will extend unemployment compensation,” he said. The debate among lawmakers, he said, is “not about whether to do it but whether to pay for it as opposed to adding it to the deficit.”

He would prefer to make the tax cuts permanent because the current, 10-year-old tax rate “is appropriate,” he said. But “the president won’t sign a permanent extension.”

“I’m very hopeful that the tax rates won’t go up,” he added, signaling his belief that the White House has abandoned its efforts to raise taxes.