Occasional attempts by the White House to change that dynamic, by inviting key legislators to dinners or the like, typically have faded fast.
Obama's first golf game with House of Representatives Speaker John Boehner, a Republican, came about only after the president had been asked repeatedly why he hadn't invited a fellow lover of the game to tee off. The outing was never repeated.
Last week, the No. 2 Republican in the Senate, John Cornyn, told a home state newspaper he never had gotten a call from the president, "which is kind of amazing to me."
Boehner and Senate Majority Leader Mitch McConnell took it as an insult when the White House issued veto threats just as lawmakers were taking the oath of office for the new Congress.
"He could have waited a few hours," the speaker said.
While Obama has a "rock-solid" relationship with Senate Democratic leader Harry Reid, former aide Jim Manley says even they aren't particularly friendly.
White House press secretary Josh Earnest dismisses the intense interest in Obama's chemistry with congressional leaders. "We're focused a little less on sort of the charm and more on the substance," he says.
Trust and good will lubricate the legislative process and any negotiations between Congress and the White House. It's possible to do a deal without them, but it's a lot harder.
Nancy Pelosi, the top Democrat in the House, credits Obama for going overboard to try to build positive ties with Republicans.
Plenty of legislators from both parties talk wistfully about the presidency of Democrat Lyndon Johnson, who was unafraid to tangle, cajole and horse-trade with legislators to translate big ideas into law in the 1960s.
But Cornyn describes Obama as "so detached and disengaged and apparently disinterested in doing the grind work that goes along with passing legislation that it would be hard to do anything."
It's always nice to get along, but voices from both Congress and the White House caution against attaching too much importance to the idea.
"People read way too much into personalities and all that stuff," says Sen. Bob Corker. "Despite what the American people think, there are a good many adults up here that understand that regardless of how you may feel personally about a situation, we have a job to do."
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Associated Press writers Nancy Benac, Matthew Daly and Connie Cass contributed to this report.