Just two words of advice: Emulate Eisenhower.
Dwight D. Eisenhower is regarded as the boring president of a boring decade. In fact, those times—with major crises in Taiwan, Eastern Europe, and the Middle East—were scarier than ours. Ike also had to close out a stalemated war, bring West Germany into a fledgling NATO, and cope with the threat of nuclear annihilation by the Soviets.
And Eisenhower made it all look boring by projecting calm and playing golf, eschewing dramatic gestures and grandiose reforms, and governing resolutely from the center. He understood that a president can more easily do harm than good, that a strong leader nurtures rather than fractures consensus, and that power has its own natural hydraulics, which not even a president can defy.
Instead of a dramatic visit to the Republican caucus with nothing to offer, Obama could have come with a list of the things in the bill that he believed were inconsistent with its stated stimulus objective and with an offer to mediate with his Democrat colleagues to see how many of those provisions he could get removed before the vote in the House and now in the Senate. As Gil Troy shows in Leading from the Center: Why Moderates Make the Best Presidents, moderation is not about splitting the difference between extremes; it is a coherent strategy all its own and one that has succeeded better than flashier alternatives. Exhausting eventfulness solves few problems. Obama needs to destabilize less while solving more. Like Ike.