During his campaign, Crawford softened criticism of health reform and, in an about-face from his first race, said he supported a 5 percent tax on millionaires to help address the budget deficit. Two years earlier he'd pledged to never support a tax increase.
Speaking to The Associated Press on Tuesday night, Crawford said he hoped the parties can find common ground.
"There's opportunities to find partnerships across the aisle and that's really what it's going take," he said. "I hope that the president will come back to Washington with that attitude. I think we're going to come back to Washington with the attitude that we're going to move the country forward in the right direction and look for opportunities to work together in that regard."
A spokesman for 3rd District U.S. Rep. Steve Womack didn't respond to an interview request Wednesday.
In a statement issued after he was declared the winner over two small-party candidates Tuesday night, Womack said the country is at an important juncture.
"America is at a tipping point, and now, more than ever, we must come together to pass real reforms — including restoring fiscal discipline, regulatory burden-relief, and corporate tax reform — to create a stable economic environment that will encourage businesses to expand, create new jobs, and, ultimately, get America back on track," Womack said.
Womack, who represents northwest Arkansas, claimed 76 percent of the vote Tuesday, with Green Party candidate Rebekah Kennedy getting 16 percent and Libertarian David Pangrac getting 8 percent, according to returns that showed 88 percent of precincts reporting.
Crawford defeated prosecutor Scott Ellington, a Democrat, 56 percent to 39 percent, while Cotton won against state Sen. Gene Jeffress, 59 percent to 37 percent. In the tightest of the seemingly easy races, Griffin beat Democrat Herb Rule, 55 percent to 39 percent.
Arkansas didn't have a U.S. Senate seat on the ballot this year. The lone Democrat, Sen. Mark Pryor, is up for re-election in 2014 and has said he is running.
Griffin has been mentioned as a potential rival to Pryor in 2014, but said Tuesday night that he was focused on his job in Congress.
Associated Press writer Jeannie Nuss contributed to this story.
Contact Chuck Bartels at www.twitter.com/cbartelsLIT