Pointing to a GOP faction tying the defunding of the Affordable Care Act and the funding of the government, Kasich said, "When you don't control the White House or the U.S. Senate, you are not going to kill the administration's major policy objective."
He said the relationship between Democrats and Republicans is at an all-time low in Washington, citing a "lack of cohesiveness [and] respect, and it's across the board."
During a panel discussion Wednesday at the Scottsdale conference, Texas Gov. Rick Perry of Texas said "talking to people's hearts is [the] messaging part of it."
Perry, joined by Kasich and Oklahoma Gov. Mary Fallin, said he believed immigration would change substantially over the next 18-to-24 months, suggesting the discussion would be "where are we going to find enough people to fill all the jobs that we are helping to create in this country because everyone who had came over here illegally looking for a job to take care of their family is going home."
Kasich said Republicans also should focus on a message of caring and connecting with voters as much as putting people back to work.
"You can't ignore people who live in the shadows ... you can't let people get stuck on the other side of the bridge to prosperity," Kasich said. "People have to know that you care about them, that you understand them."
"And if we can demonstrate more of that, people will say that's kind of a new brand for Republicans, create jobs, compassion, care," he said.
RGA leader Gov. Bobby Jindal of Louisiana made a similar observation during a separate news conference, ABC News said.
"We have to do a better job of defining what we are for [and not] outsource our brand management to D.C.," Jindal said. "We have to win the war of ideas, too often in D.C. we are defined as the party of no, too often we are defined about what we are against."
New Jersey Chris Christie will take over the RGA leadership this week.
Notable deaths of 2014 [PHOTOS]