Washington (CNN) -- When Republican Trent Lott sat down for lunch with Democrat Tom Daschle on Monday afternoon, mere hours before voters shellacked President Obama and his party in the midterm elections, it was more than just two former Senate gladiators getting together to reminisce about old times
Despite their many differences over the years, Lott and Daschle managed to find a way to work together during the bruising days of the Clinton and Bush administrations, where everything from impeachment to Iraq caused deep divisions between the parties.
"He and I are whispering back and forth," Lott told me of his conversations with Daschle.
The two still keep in close touch and are now working back channels to try to get Obama and incoming House Speaker John Boehner, R-Ohio, to see that a divided government does not have to mean that the government comes to a screeching halt.
"Tom and I went through this situation on both sides," said Lott, who was the Senate majority leader while Daschle was minority leader. "We've been through three different iterations of circumstances where we found a way to get things done."
When Republicans took control of Congress in 1994, President Bill Clinton was still able to get a balanced budget and major welfare reform.
Lott and Daschle later hammered out a historic power-sharing agreement when George W. Bush was elected in 2000 with a 50-50 Senate. They ended up passing the president's tax cuts and signature No Child Left Behind education reform law, among other big initiatives.
And finally, after Bush's party lost both chambers to Democrats in the 2006 midterm elections, Lott worked with Daschle's successor, Senate Majority Leader Harry Reid, D-Nevada, to come together to pass many of the 9/11 Commission's recommendations for intelligence reform and the first increase in the federal minimum wage in a decade.
"There are things you can do together," Lott said. "It doesn't have to be blood and guts every day. The rhetoric is over, now what are you going to do?"
It's the question hanging over Obama: What will he do next? And besides Lott, there are other senators who served with him on Capitol Hill who believe he will follow in the footsteps of Clinton and retool his message and move to the center.
"I think it is really incumbent on him to try and work with the Republicans," said former Sen. Mel Martinez, R-Florida. "Everyone talks about almost a reset button. You have to recognize you're not going to get it all your way. And the country is better for it."
Martinez says the president should pick off a couple of issues -- like a scaled-back energy reform bill and education reform -- and force Republicans to meet him halfway because they are on a short leash with voters as well. "I mean, you can't gridlock the place for two years," he said of both parties. "I think the key is to find two or three things that are not monumental and get them done."
The thinking is that this will build momentum for bigger issues, and it's a philosophy that, in the early hours after this election, is being embraced by some senior White House officials who see a chance to forge bipartisan agreement on various trade deals.
But it's clear the compromising attitude from the White House will extend only so far. The expectation among senior Democrats and Republicans is that Obama will acknowledge the need for some kind of move to the middle, but he is also expected to dig in on his principles and not give ground on making major changes to his health care reform or Wall Street reform packages.
"What voters told us in 2008 and 2010 is they're frustrated with Washington -- both times," a senior White House official said. "And what that means is we have to work together for them. [Republicans] will say they have a mandate to erase everything done over the last two years. That would be a total misreading of the situation."
Democratic officials say we should expect a statement from Obama on Thursday before he leaves on a trip to Asia. Look for him to call for a bipartisan summit with congressional leaders later this month, possibly at Camp David, an idea first pushed by moderate Sen. Ben Nelson, D-Nebraska, in a letter to the president last month.
"What's more important than the outcome of this election is that the Democrats and Republicans find a way to work together for the good of the country," Nelson said in a telephone interview.
Sharp campaign rhetoric
But getting both sides to sing "Kumbaya" is not going to be easy after a bitter campaign in which the president decided to elevate Boehner by relentlessly attacking his economic plan, while White House officials openly slammed the Republican leader as a tool of lobbyists and other special interests.
Boehner's hands, of course, are not clean either. The primary reason that Obama has thus far pushed through most of his agenda with essentially Democratic-only votes is because Boehner, and Senate Minority Leader Mitch McConnell, R-Kentucky, have spent the past 22 months saying "no" to just about every Obama initiative.
"We're going to do everything -- and I mean everything -- we can do to kill it, stop it, slow it down, whatever we can," Boehner recently vowed about blocking the Obama agenda.
A far cry from the warm words each side expressed after Obama's midnight call of congratulations to Boehner Tuesday. White House spokesman Robert Gibbs said the president was "looking forward to working with him and the Republicans to find common ground, move the country forward and get things done for the American people."
Boehner's side was also using all the right words, putting out a written statement saying it was a "pleasant conversation" and noting they discussed "working together to focus on the top priorities of the American people, which Boehner has identified as creating jobs and cutting spending."
It sounds good, but there are plenty of hurdles to following through on the promises to work together, especially with battles still looming over contentious issues such as whether to extend all of the Bush tax cuts -- including those for families earning more than $250,000 a year -- not to mention Boehner's vow to either repeal or at least radically scale back Obama's health care reform package.
On the conservative side of the spectrum, so many Tea Party favorites winning seats in the House and Senate enter the arena with the inclination to stake out principled ground on the right. "The influx of new people who will not want to compromise out of the box makes the leaders' job that much harder," Daschle says.
But there will also be pressure from the left, on Obama and leaders like Reid, to hold true to progressive principles and not moderate. Look at the tweet that former Clinton Labor Secretary Robert Reich sent Tuesday night: "Repeat: Obama's next step isn't to 'move to the center.' It's to have greater courage of conviction."
Division among Democrats
It will be difficult for Obama to steer too far to the left, however, after conservative Blue Dog Democrats took a beating in the election for not sticking to the center on the economy and health care, among other issues. No fewer than 23 of 46 incumbent Blue Dogs were defeated at the polls, sending an unmistakable message to the surviving conservative Democrats who are facing voters in 2012 that they better be careful about casting liberal votes on key legislation.
Take Sen.-elect Joe Manchin of West Virginia, who helped Democrats keep control of the chamber by running sharply against Obama. Manchin ran a television ad in which he literally shot a bullet into a copy of cap-and-trade legislation to show his independence.
Manchin did not win a full six-year term, instead getting the final two years of the late Democratic Sen. Robert Byrd's term, which means he will face the voters again in two years. "He's going to be voting with us most of the time if he wants any hope of being re-elected in 2012," a senior Republican aide said.
Then there's Nelson, who took a lot of heat back home for voting in favor of both the stimulus and the health care bill, and is expected to face a strong challenge in 2012. Since Democrats will have anywhere from 51 to 53 seats in the chamber, depending on final results in Colorado and Washington, they will be several votes shy of the 60-vote supermajority needed to pass most legislation, and the math will only get more difficult when Nelson decides to vote with Republicans on various issues.
"You've got Ben Nelson there sitting in Nebraska, and he's in trouble on a good day, so you've got that wild card," former Nebraska Republican Sen. Chuck Hagel said in an interview. "It puts him in a tough spot on all the big issues."
Nelson rejects the notion that he's in as much trouble as his critics suggest. But he does make it clear that he will not be a rubber stamp for the White House on the Bush tax cuts for the wealthy, a sign of how difficult it will be for Obama to find consensus unless he moves to the center.
"I want to see them all extended," Nelson said of the tax cuts for people making below and above $250,000 a year. "One year is too short -- at least two years" he said of the extension period that has previously been rejected by the president.
Hope for bipartisanship
Hagel, who was always an iconoclastic Republican during his time in the Senate and is now close to Obama as co-chair of the President's Intelligence Advisory Board, is hopeful that all of this pressure will help lead to the White House starting over with Republicans.
"You're going to see a whole different outreach, a Clintonian post-1994 approach," Hagel said. "They're studying what happened there, and I think you're going to see some shifts."
Clinton's approach not only helped him forge deals in the short term, but it also sealed his re-election two years later, which raises the question as to whether there is really an incentive for Republicans to work with Obama.
But all of the current and former senators interviewed for this article said that Boehner and McConnell -- who recently suggested that his top concern is making sure Obama is a one-term president -- are under pressure themselves to show results unless they want the angry electorate to turn on them.
"All this bravado and beating of the chests by McConnell and Boehner -- that runs into the wall of responsibility and accountability to govern this country," Hagel said. "The overriding issue is why can't these guys get together and fix our problems in an adult way? Republicans can't just beat their breasts. If Mitch or Boehner play those games, they're going to be in a lot of trouble in 2012."
A key player to watch in all of this is Obama's new chief of staff, Pete Rouse, who was Daschle's top aide during the time he worked with Lott on so many bipartisan compromises.
Lott fondly recalls the days when he and Clinton would fight over policy while actually developing a warm personal relationship, a bond that does not exist right now between Obama and any of the other leaders, particularly Boehner. "The first step is communication," Lott said. "When Clinton had something on his mind, he'd call me at the house 9 p.m., 11 p.m., 2 in the morning. Literally, he called me one time at 2 o'clock in the morning about El Salvador. And when we were finished, my wife said, 'What was that about?' And I said, 'I'm not really sure.' "