House Majority Whip Kevin McCarthy, who joined Obama for lunch Wednesday along with fellow Republican leaders, described the process as two sides "kind of feeling each other out."
"From where we were earlier to then, at least it's a better situation to where we're talking," McCarthy said, speaking hours after the lunch on the Ralph Bailey Show on KNZR-AM in his home town of Bakersfield, Calif.
Not that these are exactly breakthrough moments. Health care, for instance, did not even come up at the Wednesday lunch, according to participants.
Neither side appears eager to offer major concessions or spend more time together than absolutely necessary. Obama, who has never enjoyed the schmoozy side of politics, has enlisted help - bringing along the gregarious Vice President Biden and, at least on Wednesday, new chief of staff William M. Daley, both of whom have long-standing relationships with GOP leaders.
For Obama, the get-togethers are a chance to appear moderate and post-partisan as he heads into a reelection campaign in which his opponents plan to cast him as a champion of European-style socialism. And Republicans know they must show that their new power can lead to tangible policy achievements.
Both sides see room for compromise in pushing to ratify free-trade agreements, cut spending and remake the country's education system. That means looking for a bit more intimacy than some of their past bipartisan sessions, which have been marked by testy exchanges and snarky retorts - and helped spur hostility.
"The more we can humanize each other, the better it is," said freshman Rep. Reid Ribble (R-Wis.), who downed bratwurst and cheered on the Green Bay Packers as he chatted with Obama at the White House Super Bowl party.
Even so, both sides apparently also recognize the risks of angering their respective bases if they appear to be getting too cozy with each other.
When news surfaced that newly elected Sen. Pat Toomey (R-Pa.) had also accepted an invitation to the football festivities, a headline on the conservative blog Hot Air read: "Obama's Super Bowl Party: Should Pat Toomey Attend?"
Those perils may explain why the details of the new round of interactions are being held tightly.
Senate Minority Leader Mitch McConnell (R-Ky.) was mum after he lunched Feb. 4 with the president and Biden at the White House. No one even knew about it until four days later, when then-White House press secretary Robert Gibbs mentioned in passing at a briefing that "we had Senator McConnell in, I think, late last week" as part of an effort to "do better to reach out and have those discussions."
Official accounts of the interactions from the White House and GOP offices are purposefully vague, with boilerplate language about seeking "common ground."
On Wednesday, a group of six - Obama, Biden, Daley, McCarthy, House Speaker John A. Boehner (Ohio) and House Majority Leader Eric Cantor (Va.) - dined without their staff. They talked trade, economics, jobs, education, regulations and foreign policy.
"A very good lunch, and we're able to find enough common ground," Boehner said.
"Very constructive," echoed Gibbs.
Behind the scenes, participants said, Obama tried to turn on some charm. At one point the president tried abruptly to draw a personal connection with McCarthy by telling a story about a visit years ago to the congressman's home town.
"Out of the blue . . . he says, 'Bakersfield. I've been to Bakersfield,' " McCarthy told KNZR.
The president said that while he was a student at Occidental College in Los Angeles, he had borrowed a friend's car to drive to San Francisco. The tire blew out near Bakersfield, and Obama, with no credit card and little cash, walked into town to hitch a ride.
"He remembers Bakersfield being very kind to him and the people being nice," McCarthy said.
Obama urged his guests to enjoy dessert after a meal of salmon, salad, fruit and cheese. "They brought in some little apple thing the president really liked," McCarthy told Bailey in the Wednesday interview. "He was telling everybody they should eat it." The congressman said he refrained because he's trying to lose weight.
Obama also displayed a bit of White House hospitality Feb. 2 to McCain (R-Ariz.), his 2008 rival who has emerged as one of the president's fiercest critics on economic and immigration issues. It was only their second one-on-one session since the presidential race, and a McCain aide described the tone as "friendly." The conversation was "all business," on border and spending issues, but the McCain aide said Obama greeted the senator "in the hallway and escorted McCain into the Oval himself."
At the Super Bowl party, the president and first lady, dressed casually, spent most of the evening mingling separately with guests, moving about in the East Room.
Obama spent a few minutes chatting with Toomey's 10-year-old daughter about school. He also told the newly elected senator that he wanted to "get some things done" and work with Republicans if they would "meet him along the way," Toomey recalled.
Twice, Ribble and his wife looked up to see the president bounding over to his table.
"He sat down right next to us," Ribble said. "We had conversations about how the game was going. . . . I tried to bait him, but I couldn't get him to take sides."
At one point, Obama brought some snacks over, Ribble said, and noted the Wisconsinites were drinking Hinterland, made by a Green Bay brewery. " 'That's your local brew,' " Obama said to the group, Ribble recalled. "â'But make sure you try the White House brew.' He was pretty proud of what they make right there in the White House."
The White House Honey Ale, Ribble said, was "medium bodied" and "a little sweeter than normal."
Perhaps just the taste Obama was looking for.