If you wonder why President Obama has changed course and is suddenly reaching out to Republicans in Congress, you need look no further than the recent wave of public-opinion surveys, which show his approval rating dropping precipitously, his reelection bump gone. Even though polls show the public is more likely to blame Congress for the obstruction that led to the sequester and the hardship it causes, that doesn’t mean Obama gets a free pass.

Spokesman Jay Carney was at pains Thursday defending the decision to suspend White House tours in the face of a plea on Facebook from a group of disappointed sixth graders scheduled to visit Washington next week. Reporters demanded to know if the Easter Egg Roll would be next on the chopping block, a line of questioning that suggests the focus of public outrage may not play out like the president expected.

With his public strategy falling flat, Obama hit the reset button. The White House made the calculation that the president has nothing to lose and potentially a lot to gain from engaging with not only Republicans, but Democrats, too, who for the most part he has held at arm’s length. “At long last, he’s actually getting serious about working the Hill,” says Jack Pitney, a former congressional staffer who is now a professor at Claremont McKenna College in California. “It takes a lot of effort, but as other presidents have learned, you can get a lot done if you work with lawmakers.”

It took Obama a long time to recognize the value of personal interaction with members of Congress. He’s not a naturally social person and prefers to spend downtime with family and friends. During his first two years in office, he tried to build bipartisan relationships, but they were purely of a business nature. He didn’t put any real effort into socializing with lawmakers, which they interpreted as arrogance on Obama’s part and a lofty disdain for what he considers the grubby side of politics. So sitting down with Republicans away from the White House, in what Carney called “neutral territory,” ordering wine and kibitzing, could usher in a whole new chapter in the Obama presidency.

Obama’s schmoozefest began over dinner Wednesday evening with 10 Republican senators at Washington’s Jefferson Hotel. South Carolina Sen. Lindsey Graham put the guest list together, and Obama picked up the tab, using his own money, not taxpayer funds. The next day there was lunch at the White House with House Budget Chairman Paul Ryan and ranking Democrat Chris Van Hollen. Next week Obama goes to Capitol Hill to meet House and Senate Republican and Democratic caucuses.

The flurry of activity was applauded by both parties, though everyone is skeptical that it will result in the grand bargain that Obama wants, at least in the short term. Still, says Brookings Institution senior fellow William Galston, “it’s worth testing the proposition that there is enough disagreement within the Republican Party to make a serious fiscal conversation possible.” Everyone on Obama’s dinner list has expressed frustration with their party, making them likely members of what Obama has dubbed the “common-sense caucus.”

A House GOP aide thinks Obama initiated the outreach because he overplayed his hand on the sequester and the criticism stuck that he was campaigning around the country instead of meeting with members of Congress. Still, says this aide, “it’s exceedingly difficult to jump-start relationships ... If the president sustains this effort over the coming months, we could see success. But if he throws up his hands and says, ‘I had lunch with Paul Ryan, and they still wouldn’t raise taxes,’ then this will be seen as a transparently ... political maneuver.”

Just a week ago, Obama was protesting that he couldn’t make the Republicans do anything, that he couldn’t lock them in a room. If this new tactic has any hope of working, he’ll have to keep at it longer than he might like and without any immediate return. But if he perseveres, he could put real pressure on the Republicans to respond. “You have to go beyond a first meeting to pass the test of seriousness, but if the president takes one or two more steps, then the ball will be in the Republican court,” says Galston, who was President Clinton’s domestic policy adviser during the standoff over government spending in the ’90s.

House Speaker John Boehner has declared publicly that he won’t negotiate directly with the White House, and he has said the Senate should go first in future fiscal bills, conceding he can’t bring legislation to a vote in the House without a strong headwind from the Senate. “Does the White House think any deal would be made without the Speaker of the House? Really?” a GOP House aide emailed incredulously. The answer is no, but Boehner will be the last one on this train, by choice, which is how he keeps his speakership.

By taking more of a leadership role, Obama will have to do more than talk in broad terms about reforming entitlement programs. “We know what he does when he really wants something—he campaigns on it,” says Jim Kessler of the centrist-Democratic group Third Way. If Obama demonstrates a willingness to really deal on entitlements, he might persuade Republicans to overhaul the tax code in a way that closes loopholes and caps deductions. That’s the deal that must eventually be made. The sequester failed to force the compromise as it was supposed to do, but there’s still time, says Carney, who sums up the president’s strategy this way: “He’s trying to make something good out of a bad situation.”