Within the party, Democrats are deeply split over which is the best course. “There are two schools of thoughts. A school of thought to try and reach common ground, and one to just be defiant and hold off and point to the other side,” said former Senate Majority Leader Tom Daschle, who serves as an informal adviser to the White House.

A divided government could lead to gridlock. One leading liberal lawmaker, Rep. Henry Waxman, said he couldn’t see how the two parties could reach a deal on deficit-cutting “if we’re going to cut spending without increased revenues.” He said if the GOP gains power and is unwilling to compromise then Mr. Obama’s options will be limited. “I don’t think [Mr. Obama] has the full choice in the matter,” Mr. Waxman said. “It has to do with whether he has a partner.”…

Working with Republicans carries risks for the White House. The Democrats’ liberal wing is already frustrated by what they see as compromises made during the opening half of his term. Now liberals are arguing for resisting Republicans, saying Mr. Obama will deflate his base voters if he signs onto any agreement that, for example, pares Social Security benefits.

“That would be a war within the Democratic party,” said Roger Hickey, co-director of the liberal group Campaign for America’s Future.