When former U.S. Sen. Sam Nunn needed a partner to push for federal funds to dismantle nuclear weapons in the former Soviet Union, the Georgia Democrat turned to Republican Sen. Richard Lugar of Indiana.
Working together, the two produced the Cooperative Threat Reduction Program in 1992, an initiative aimed at reducing the stockpile of nuclear bombs as well as biological and chemical weapons following the breakup of the Soviet Union at the end of the Cold War.
Likewise, then-President Bill Clinton, a Democrat, reached across party lines a few years later when he made GOP Sen. William Cohen of Maine his second-term defense secretary.
With that kind of bipartisanship missing in Washington today, it's no coincidence that Nunn and Cohen are among the leading Democrats and Republicans who will be gathering on Monday at the University of Oklahoma for a meeting that could lead to a third-party centrist challenge in this year's presidential race.
Besides Nunn, the Democratic side includes former Oklahoma Sen. David Boren, the host for Monday's session, ex-Florida Sen. Bob Graham and former Sen. Gary Hart of Colorado.
Republicans expected to join Cohen include former Missouri Sen. John Danforth, ex-New Jersey Gov. Christine Todd Whitman and Sen. Chuck Hagel of Nebraska, who is still in the Senate but is leaving office at the end of this year.
"We have a lot of polarization in the country. It's very difficult for Democrats and Republicans to work together," said Merle Black, a political science professor at Emory University. "That's the frustration these people, mainly former office holders, feel.
"Many have worked behind the scenes with members of the other party. They're discouraged today because they no longer see that happening."
The session could lead to something more than an exercise in hand-wringing.
Former New York Mayor Michael Bloomberg, who also is expected to attend, has been traveling the country making policy speeches since pulling out of the Republican Party last summer and declaring himself an independent.
While Bloomberg hasn't said he will run for president as an independent or third-party candidate, he is a multi-billionaire with the resources to launch such a bid.
At a minimum, the attendees are expected to produce a joint statement encouraging the current crop of presidential hopefuls to take a bipartisan approach to the pressing issues of the day.
But if members of the group don't see that happening, Monday's session could set the stage for a centrist candidacy by Bloomberg or some other political moderate.
Black said the odds are stacked against Bloomberg or any other third-party or independent candidate because of the way American presidential elections are structured.
"Our party system is based on carrying states," he said. "In order to do that, an independent candidate would have to run ahead of the Democratic and Republican candidates. That's very hard to do."
Black pointed to 1992, when Ross Perot, another wealthy independent presidential hopeful, won 18.8 percent of the vote against Clinton and President George H.W. Bush - the best showing of a non-major party candidate in decades - but didn't capture a single electoral vote.
"It's hard to see any state where someone like Bloomberg, who is largely unknown outside of New York, could run ahead of the Democratic and Republican candidates," Black said.
Of course, Nunn, Cohen and the other moderates don't have to backstop a successful independent presidential candidate to exercise some influence over the campaign being waged by the Republicans and Democrats already in the field.
But Black said the group's timing for affecting the tone of the debate is off. Monday's meeting falls at the beginning of the primary and caucus seasons, between last week's kickoff in Iowa and Tuesday's showdown in New Hampshire.
Black said the fiercest stage of the primary contests is not the time to try to convince major party candidates to show their bipartisan sides.
"That's the last thing they're going to do in the middle of the primaries," he said.
On the other hand, voters in Thursday's Iowa caucuses showed the current system may not be as broken as the organizers of Monday's meeting seem to believe.
Republican and Democratic caucus-goers chose former Arkansas Gov. Mike Huckabee and Illinois Sen. Barack Obama, respectively, two candidates who have been among the most outspoken about the need to find bipartisan solutions to the nation's problems.