(CNN) -- House Minority Whip Eric Cantor issued a warning Wednesday to Republicans after the party's takeover of the House of Representatives in the midterm elections.
"This is a second chance for us," he told CNN. "If we blow it again, we will be in the wilderness for a very long time. We have to deliver."
Cantor, who described himself as "energized" despite only three hours of sleep, said the overall message from Tuesday night was a repudiation of Democratic policies, including health care reform.
Cantor is expected to replace Democrat Steny Hoyer in January as the next majority leader, the second-ranking position in House leadership.
Meanwhile, in an emotional speech Tuesday night at a GOP election rally in Washington, the presumptive speaker of the House, Rep. John Boehner of Ohio, told a crowd of supporters, "This is not a time for celebration."
Boehner said, "It is a time to roll up our sleeves and go to work. We can celebrate when small businesses begin hiring again. We can celebrate when the spending binge here in Washington has stopped. And we can celebrate when we have a government that has earned the trust of the people that it serves."
Yet while reading election results at the same rally earlier Tuesday evening, Republican Rep. Greg Walden of Oregon betrayed a bit of his party's excitement at being back in the majority when he quieted down the crowd by saying, "I know it's a party."
Judged only by what they said, many candidates seemed to agree with Boehner's assertion that Tuesday's victories were more a call to action than a reason to celebrate.
"Tonight we're going to celebrate all that we have accomplished in this campaign," Sen.-elect Kelly Ayotte of New Hampshire told a crowd in Concord, "but tomorrow we begin the important work of getting our country back on track."
Former Sen. Dan Coats of Indiana was similarly somber about the voters' decision to return him to Washington after more than 10 years in the private sector.
"Tonight we celebrate, but with tomorrow's dawn come responsibilities," Coats said at his victory rally in Indianapolis. "For me, the responsibility is you. Because I've been chosen by the people of Indiana to stop reckless spending to fight for our national security, to fight against a government takeover of health care and to fight for every Indiana job, and that is exactly what I will do."
From a policy perspective, many candidates echoed Coats' call for fiscal responsibility and smaller government. Several newly elected legislators promised Tuesday night that their responsibility in Washington was to keep government out of the private sector's way.
"Government does not create jobs," said Rand Paul, newly elected senator from Kentucky. "Individual entrepreneurs, businessmen and women create jobs, but not the government."
Ayotte touted her history in small businesses to make the same point, saying, "We appreciate that it's not the government that creates the jobs in this country."
But perhaps the elections of Coats and former U.S. Rep. Pat Toomey to the Senate best epitomized the House GOP leadership's theme of the night: Tuesday's victories should be seen as the Republican Party's second chance.
As the victories began rolling in, GOP Whip Eric Cantor of Virginia told CNN, "I'm very excited, as are most in our Republican conference, to be given this second chance. Now we've got a golden opportunity as Republicans to set the record straight, to actually say we're going to listen to the people, which is what the vote tonight is about."
Rep. Mike Pence of Indiana, chairman of the House Republican Conference, released a statement earlier that said, "Republicans have not just been given a new majority in Congress, Republicans have been given a second chance."
Striking a similar tone, Sen.-elect Marco Rubio of Florida issued a somewhat harsher condemnation of the current Republican Party during his victory speech in Coral Gables.
"We know that tonight the power in the United States House of Representatives will change hands," Rubio said. "We know tonight that a growing number of Republicans will serve in the Senate as well, and we make a grave mistake if we believe that tonight these results are somehow an embrace of the Republican Party. What they are is a second chance. A second chance for Republicans to be what they said they were going to be not so long ago."
Despite such significant gains in both the House and Senate, many of the GOP's most high-profile victors on Tuesday night were notably restrained. They were perfectly comfortable criticizing President Obama and "Washington" more broadly, but most were hesitant to praise Republicans.
Perhaps Paul, a candidate who received substantial support from national Tea Party groups, explained it best when he began his victory speech by promising to ask his new colleagues in the Senate to deliberate on this: "Eleven percent of the people approve of what's going on in Congress, but tonight there's a Tea Party tidal wave, and we're sending a message to them."
At a time when most polls show that Congress' approval rating is at a historic low, even Boehner -- a 10-term incumbent who's in his second stint in his party's leadership -- made certain to promise that his "new majority will be prepared to do things differently, to take a new approach that hasn't been tried in Washington before by either party."
CNN's Brianna Keilar and Ed Hornick contributed to this report.