Two influential Democrats, speaking separately here, intriguingly offered a similar answer. Rather than compromising more, they suggested, Obama would try harder to mobilize the American people to pressure Republicans in Washington.

Valerie Jarrett, speaking at a Bloomberg News forum Tuesday morning, blamed the divisions of the first term entirely on the opposition.

“We’ve had four very tough years when it’s been very difficult to get Republicans to the table,” she said.

Obama’s mistake was not in his policies but, she said, in failing to generate more pressure on Republicans, who “ignored their constituents.”

“The country doesn’t have to center in Washington,” Jarrett said, adding later: “I think what we probably would do over again is, in that first year, spend more time outside of Washington with the American people and telling our story around the country and really galvanizing the pressure that needed to be put on the Republicans of Congress.”

Sen. Charles Schumer (D-N.Y.), one of the party’s top political strategists, told me he hasn’t talked with Jarrett about this. But in a meeting with Post reporters and editors Tuesday morning, he offered a similar diagnosis and prescription.

“He didn’t go to the outside enough,” Schumer said. “He played too much of an inside game. He sat with Republicans around the table and said, ‘Let us compromise.’ ”

In a second term, Schumer said, Obama would go to the people as President Ronald Reagan did to pressure Democrats in Congress to pass the tax cuts Reagan wanted.

“You will see a different kind of president in some ways,” Schumer predicted. “He will go to the public more. He will be more realistic about what they [the hard right] are trying to do.”

Could such a strategy work? Schumer argued that, while moderate Republicans have been pretty much eliminated from the party, the GOP congressional delegation is evenly divided between “mainstream conservatives” and a far-right, tea party wing. If in November, Obama wins, Republicans lose a few seats in the House and Democrats maintain a narrow Senate majority — Schumer’s forecast — then Obama’s “outside game” could help persuade mainstream conservatives to buck their right wing, Schumer said, and make possible the deals many of them quietly favor. That would be especially true if far-right Senate candidates lose in Missouri or Indiana.

But can an outside game promote the kind of policies that the country will need in 2012 to solve its fiscal crisis, policies that are likely to be far less popular than are tax cuts?

“I think it’s going to be hard,” Schumer acknowledged