At the same time, Senate Majority Leader Trent Lott promised a probe into the allegations of Democratic campaign financial misdeeds that Bob Dole raised in his losing bid for the White House. "We have a responsibility in a variety of ways to take a look at ... what appears to be wrongdoing," he said.
But another round of Whitewater hearings? No, says the Senate Banking Committee chair, Alfonse D'Amato (R-N.Y.), who also headed the special Senate panel that delved into the Clintons' ties with the owners of a failed S&L and subsequent dealings.
"We should leave that in the hands of the special prosecutor, and shouldn't be attempting to substitute our judgment," D'Amato said yesterday.
"It's not the time to be looking at investigations, either by the banking committee or any other" Senate panel, he said.
Clinton, too, sounded hopeful that he and the GOP Congress could work together. Referring to recent legislation that raised the minimum wage, expanded access to health care and reformed welfare, he said, "If we can somehow re-create for the next four years the spirit that prevailed in the last six weeks of the Congress, we can do great things."
Republicans are expected to take a few weeks to sort out their plans for the Congress that convenes in January, but some elements were clear even before the final votes were counted in Tuesday's undecided congressional races.
In an interview, Gingrich renewed his promise to have a constitutional amendment on term limits as the first substantive issue on the House floor next year.
Lott, at a news conference, suggested a balanced budget amendment to the Constitution might be voted on early, as well. That passed the House in 1995, but failed by a single vote in the Senate, with Clinton lobbying lawmakers to oppose it.
"It looks like we might have the votes to pass it" when the newly elected senators are sworn in, Lott said, although he also predicted that some former Democratic supporters would be under pressure to switch their votes.
Gingrich said he had spoken by telephone with Clinton during the day, and the GOP leaders "want to sit down with him" next week before they begin mapping their agenda.
"It is the American system that after the election you figure out how to get things done," said the Georgia Republican, who spoke harshly of Clinton during the campaign.
Lott will be presiding over a strengthened GOP majority in the Senate beginning next year. With an Oregon race still unsettled, Republicans will have at least 54 seats, one more than in the expiring Congress. That likely will translate into larger majorities on some or all committees, giving the GOP a freer hand in drafting legislation.
In the House, Republicans will have roughly 10 fewer seats than last time, with the final tally awaiting the outcome of six races too close to call and three runoffs set for Dec. 10 in Texas.
It marked the first time in 66 years that Republicans had held onto a House majority. Even so, the loss of a few seats is likely to strengthen the hand of moderates in both political parties - the Republicans who want to sand down the sharper edges of their own party's agenda and the Democrats who are willing to reach across the aisle on key issues.
"The moderate-conservative wings of both parties are going to be in a very good position," said Rep. Charles Stenholm of Texas, a prominent conservative Democrat.
Rep. Christopher Shays, a moderate Republican from Connecticut, agreed. The voters decided on Tuesday that "right of center is fine, far right isn't," he said.
Indeed, the political division within the government seemed to reflect the popular mood. Election Day interviews with voters leaving their polling place showed the country was split evenly on a question of whether they trusted Congress or the president to do what's best for the country.
Congressional Democrats, who fell short in their bid to regain the House, sought solace in the outcome. "I think it's incumbent now on the Republicans and on us to try to reach bipartisan, sensible solutions to the budget, campaign finance reform ... and every day problems people face," said Democratic Leader Richard Gephardt of Missouri. Aides said Gephardt would seek another term in his leadership role.
In the Senate, Democratic Leader Tom Daschle said in a statement, "If there's a mandate in this election, it's a mandate for moderation and bipartisan cooperation."
Republicans spoke of cooperation, but distinctly on their terms.
The two sides can work together, Gingrich said, as long as the president pursues the program that won him re-election, "which after all was conservative."
House Majority Leader Dick Armey was more barbed in his comments, saying that a compromise on Medicare - a major issue in the campaign - might even be possible. "He certainly has no need to do any political work in this year, so we can get down to the policy issues that are before us, and we ought to be able to work together on that," said Armey.