Tom Daschle and Richard Lugar lived through one in the Senate in 1995. Lugar, a Republican, became chairman of the Agriculture Committee that year. And after his party's loss, Democrat Daschle took over as Senate minority leader, ascending to majority leader six years later.
Both tell Weekend All Things Considered host Guy Raz that there are ways the parties can bridge the partisan split.
"The fundamental question can be: Can we include? Inclusion is key," Daschle says. "If people feel included if they feel as if they can be invested in something that they really can point to as an accomplishment I think there's some real opportunities."
How Truman Rode The Wave
A similar tide rolled in midway through Harry Truman's term 64 years ago, but rather than bogging down Congress, it actually allowed the creation of some of the biggest foreign policy programs of the Cold War era.
The situation wasn't entirely the same the economy was doing well by comparison and the country was in relatively good spirits after World War II. But during the 1946 midterm elections, voters put Republicans in charge of both the House and Senate.
"Everyone reads it as a kind of mandate for conservatism," Princeton historian Julian Zelizer tells Raz. "The New Republic says, 'Bow your head folks conservatism has hit America.' "
Congress' new leaders had no interest in more sweeping domestic policy; the Republicans wanted to cut back programs. Zelizer says there was a sense that Truman was in retreat. Stuck with a divided Congress, the president set his sights beyond the country's borders.
And President Obama, now in the midst of an Asian tour, seems to be following the script written by Truman.
"He turns his attention abroad, where there was still a possibility that he could build a legacy for his presidency," Zelizer says.
Truman surprised people by working with Republicans, such as Sen. Arthur Vandenberg of Michigan, to implement some of the key policies of the Cold War era, including the Marshall Plan to rebuild Europe after World War II; the National Security Act in 1947 creating the CIA; and the Truman Doctrine, supporting countries that were resisting communism.
Afghanistan And A New 'START'
Today, that kind of bipartisan support on foreign policy is a possibility, says Indiana's Richard Lugar, the ranking Republican on the Senate Foreign Relations Committee.
But there are challenges: Mitch McConnell, the Republican leader in the Senate, has said his No. 1 priority is to make President Obama a one-term president.
Lugar has been in the Senate since 1977. He led efforts to dismantle nuclear arms and destroy biological and chemical weapons abroad. Currently, he's trying to get the new Strategic Arms Reduction Treaty (START) ratified.
Lugar says one area where the president and Republicans have shown signs of agreement is Afghanistan.
"Republicans have given very strong support to the administration on Afghanistan," he says. "I would not suggest that Democrats have not given support too, but the fact is that this has been much more of debate within the Democratic Party."
Another area where Lugar says both parties must agree is on the passage of the new START and he thinks that needs to happen before the next Congress is sworn in.
"I think it's very important to act promptly. We have no way of verifying precisely what the Russians are doing in terms of modifications, building of weapons, moving them, whatever might be the case. It's important that we get the verification situation straightened out immediately, and secondly, that we get back to the table again to talk about tactical nuclear weapons," Lugar says.
While some newly elected Republicans, such as Rand Paul of Kentucky, have voiced concern that the treaty could limit American anti-missile deployment overseas, Lugar says there's no basis to that fear.
"We've had 15 hearings of the Senate Foreign Relations Committee where we have looked at every aspect of missile defense," he says. "And all the testimony has said very clearly that we are not inhibited in any way in creating missile defense, whether it be based in Europe or based in the United States or based anywhere."
Getting Past 'Us Vs. Them'
Daschle says that despite the rhetoric, there are several areas where the two parties can find common ground: trade, tax policy and even some aspects of health care.
But, he tells Raz, the Republicans' current "us vs. them" mentality and talk of repealing the Obama health care plan is "going nowhere."
Neither side, he says, will compromise on principle.
"I don't think either side is capable or even should have to do that. But I think when it comes to policy, you can apply principles in a way that allows for common ground," he says.
Making that happen means the president has to reach out, Daschle says, and Republican leaders must reciprocate.
"I would love to see some Camp David sessions, I'd love to see some weekly meetings down at the White House; intense meetings on probably the first and most important thing the economy," he says. "How can we continue to improve, how can we build, how can we bring down the unemployment levels, and what can Republicans, Democrats do together to make that happen?"
He says cooperation in Congress will only start with trust on both sides of the aisle.
"Trust is built on better communication, and better communication is built on better chemistry. And the only way you achieve better chemistry is when you've got people in the room that begin the dialogue," he says. "That's really what has to happen. We've got to see more dialogue."