Rep. Dennis Ross, R-Lakeland, who was among the few freshmen members of Congress returned to office without opposition, said cooperation from both sides now has to begin.
He said it must include better working relationships with the Democrats and between the newest Republican congressmen and Republican leaders.
"Now, more than ever, healing has to begin. We know that President (Barack) Obama will be in office for the next four years, and with the election behind us, we have to work together," he said. "We have serious problems, including the expiration of the tax cut approaching. I think there will be some form of agreements."
Winter Haven lawyer Rick Dantzler, a former Democratic state senator and candidate for governor and lieutenant governor, said it is now time for congressmen to "take the poison pill" and take the pressure off the new members coming in January.
"I think the lame-duck session provides an excellent opportunity for the Republican House and the president to deal with very difficult issues," he said.
"And Speaker Boehner and the president need to do that in the lame duck session (in November and December) to get those hard-to-swallow things off the table and start clean in January" when the president and the new Congress are sworn in, he said.
Obama must work with the House, said Bruce Anderson, a Florida Southern College political science professor.
Tuesday's election may have made it easier for Republicans when the president does step forward to negotiate, he said, because they no longer have some caustic members of their party.
"People like (Indiana GOP Senate candidate Richard) Mourdock put moderates like (Gov. Mitt) Romney in a terrible position. It was clear that he was appalled by these people, but as a Republican he had to put up with them," Anderson said.
Mourdock, who was defeated, became a lightning rod for criticism after he said it was God's will if a woman became pregnant from rape.
"I think, in a very measured way, the election also silenced (outspoken Republicans) Karl Rove and Grover Norquist, and that will allow people like (N.J. Gov.) Chris Christie and others to rebuild the Republican Party," he said.
Anderson said because of the change he perceives now in the GOP House, Obama can no longer ignore negotiations.
"In the final analysis, the American people won't stand for another two years of standoff," he said. If that happens, "then these people (politicians) on both sides of the aisle are going to see a lot of angry people in two years who won't put up with it anymore."
On Tuesday, some of the 87 GOP freshman elected to Congress in 2010 were voted out of office after only one term.
"Illinois lost four freshmen aligned somewhat with the tea party, and Rep. Alan West (R-Plantation) unfortunately lost," Ross said. "They were in marginal districts, and it was that their policies didn't play well with some in the marginal districts."
Having so many new congressmen made it difficult to manage and work the system, said Ross, who entered the House with the benefit of having had eight years of lawmaking experience in the Florida Legislature.
Ross said he sees hope for a good working relationship to solve many of the financial and economic problems facing the nation, especially since there are no congressional elections in 2013.
But Paul Senft of Haines City, who recently stepped down as national committeeman to the Republican National Committee, said he is hopeful but not optimistic that the president will cooperate with congressional Republicans.
"Hopefully, the president will do what he hasn't in the first four years - work together with Republicans," Senft said. "But he won without having worked with us, so I don't have any confidence that he will change.
"I really do hope that it is going to be different in the next four years and that we can wipe the slate clean and work together."