“There’s a temptation to be very transactional in diplomacy,” Power told Fortune’s Nina Easton on Monday night at the launch of the “Smart Women, Smart Power” series in Washington, “particularly when you’re the United States and there’s a lot going on… You’re in everything. So the temptation is to go to other countries when you want something. You want what you want when you want it.”

But heeding advice from the late Richard Holbrooke, a predecessor and mentor, Power says she has carved out time to get to know her fellow envoys: taking African ambassadors to an NBA game, for example, and paying, by her count, 102 courtesy calls on different ambassadors.

“My team gives me all these points I’m supposed to ask them,” she said, adding, though, she tends to focus on getting people to talk about what matters to them. “Usually I just say, ‘When your country got independence, how’d that happen exactly?’”

The idea that a diplomat would make an effort to be diplomatic would seem so elementary that it’s barely worth mentioning. But the analog to her boss and his struggles with Congress is hard to miss. A meta-critique of Obama’s leadership at home that’s emerged from the right and a certain class of Washington commentator holds that Obama could get more of his agenda through Congress if he’d only try to build some relationships with lawmakers, using exactly the kind of outreach Power describes.

Obama’s defenders deride the argument as the “Green Lantern Theory” of the presidency — the notion that the president can summon the power to force his will upon the legislative branch, either by blunt, direct persuasion and coercion or by making a public case that overwhelms Congressional intransigence. In reality, this argument goes, no presidential charm offensive could budge opposition cemented by deep, structural forces — some in place since the Founders put them there as checks on executive overreach and others that have emerged as features of a political system that reflects a highly polarized electorate.

Obama himself has voted with his feet, declining to make more than the most perfunctory nods toward getting to know his Congressional sparring partners. Even his allies on Capitol Hill gripe bitterly about the outreach deficit, putting him in the position after the Democrats’ midterm drubbing of trying to rebuild ties to his own flock in Congress, to say nothing of newly-empowered Republicans.

Whether or not the Green Lantern theorists have a point, the fact remains Obama has enabled the debate by turning his nose up at the backslapping rituals he evidently finds distasteful and unworthy of his time.

There are no doubt major differences between the UN and our domestic political system. For one, the imperative for self-preservation is much more acute with Members of Congress who must face voters directly. But Power makes a compelling case that a human approach can go a long way to overcoming “positional warfare.” To do that, she says she tries to “understand what people are bringing to their jobs every day and their life experiences.” And she credits the approach with helping round up 100 votes in the UN General Assembly back in March for a resolution rejecting as a sham the Ukraine referendum on Russia’s annexation of Crimea. That, she said, may not sound like a heavy lift, but it marked a major improvement over the 20 votes the same body mustered to protest Russian incursions into Georgia. We’ll never know how a sustained Obama campaign at home might have improved his fortunes. But if the President understood it would yield even a fraction of Power’s charm dividend, he might have invited more Republicans over for a beer.