But unlike so many other odd-couple functions in this town, this wasn't a charity fundraiser cleverly designed to bring old adversaries together as bait for a good cause. It was a "Cease-Fire on Health Care" forum, sponsored by American University's Center for Congressional and Presidential Studies, supported by a grant from Pfizer, and moderated by former Sen. John Breaux, D-La.
And truth be told, the senator from New York and the former House speaker from Georgia discussed real substance. They focused on health care proposals they could agree on, such as increasing the sophistication of medical record-keeping.
Both politicians talked in plain English, using lines that clearly had been road-tested, in an obvious effort to make complicated points easier to understand. Almost anyone could have grasped and been intrigued by what each was saying. And anyone who didn't already know that the two had established a detente would have been surprised that they were not just treating each other civilly but actually finding common ground.
But as interesting as the substance was, the rich and plentiful ironies of the event were even more fascinating.
Twelve years ago, Gingrich and his Republican allies had pummeled the then-first lady's sweeping health care proposal mercilessly, virtually eliminating her, for a time, from any public role in formulating the policies of the Clinton administration. That pummeling helped to create an anti-Democratic wave that Republicans then rode into power, putting the GOP in control of the House for the first time in 40 years.
A few short years later -- after a sex scandal almost forced President Clinton from the White House -- Hillary Clinton watched as Gingrich lost the speakership, in part because of his own peccadilloes, in part because of a voter backlash against the GOP's impeachment of her husband.
Yet, this month, there the two battered political survivors were in the ballroom of the National Press Club, each shamelessly using the other to acquire a more mainstream image in preparation for making a White House bid.
The chief obstacle standing between Clinton and her party's nomination is a widespread fear among Democrats that she can't win a presidential general election. They worry that the public's views of her are so polarized that she would not be able to pick up enough Republicans, hold on to moderate and conservative Democrats, and win the lion's share of independents.
Gingrich, meanwhile, badly needs to persuade much of the electorate that he is not a mean-spirited ogre with fangs. He has to live down his reputation as someone who overplayed his hand, winning a majority by running as a reformer, then trying to govern from the far right -- risking the Republican majority by going too far, too fast and misreading his "mandate for change."
Conservatives swear that Gingrich desperately wants to run for president, that he has tasted power and wants it back, but that he thinks he needs to soften his edges.
So at the Press Club, each of the guest speakers was using the other, seemingly taking delight in the irony of playing a role in each other's political revitalization after political near-death experiences.
For Clinton, the appearance with Gingrich was one in a series of high-profile activities designed to firmly position her in the political center. She began by taking hawkish stands on national security and giving unquestioning support to the war in Iraq. Then, she very publicly sought a middle ground on abortion. Most recently, just days after the health care event, she assumed a leadership role in the moderate Democratic Leadership Council and delivered a major address on national security at its "Conversation" in Columbus, Ohio.
For Gingrich, the Press Club gathering was also a clear attempt to begin retooling his image. The event was patently self-serving for all involved, but it was a reminder that politics doesn't have to be poisonous. Everyone in the room seemed to enjoy the show, which provided a sharp contrast with all too many Washington events where venom is the rule and civility the exception.