The party's dilemma was in sharp relief in a Denver public television studio here, where four candidates gathered for a Republican primary debate in the race to represent the deeply conservative, rural and exurban 4th Congressional District, which covers the eastern third of the state.
All the candidates said they oppose gay marriage, want to repeal President Barack Obama's health care plan and object to allowing people living in the country illegally to become citizens.
The front-runner in the Colorado race, Weld County District Attorney Ken Buck, narrowly lost a U.S. Senate race in 2010 because he was seen as too extreme on issues like abortion and immigration. Now he has been hit in ads by state Sen. Scott Renfroe for "flip-flopping" on those two issues.
"It's one of the great ironies of Republican politics that we fall victim to," Buck said in an interview. "I'm very conservative on life, I'm very conservative on immigration, but given enough money" anyone can be attacked for not being pure enough.
Renfroe said: "We need candidates who will stand firmly for what they believe."
Immigration was an issue singled out by a GOP-commissioned "autopsy report" last year that analyzed Romney's loss to Obama. The report said Republicans must embrace "comprehensive immigration reform"— Washington shorthand for legalizing the immigration status of those living here illegally—to improve the GOP's strained relationship with the fast-growing Hispanic and Asian electorate.
The recommendations quickly hit resistance from congressional Republicans who rely on primary voters strongly opposed to "amnesty" for immigrants living here illegally.
The resistance might have softened if Republican lawmakers felt threatened by public disdain for the 2013 government shutdown or by worries of midterm election setbacks this fall. Instead, the shutdown issue faded, and Republicans are having a good primary season.
With all cylinders firing, "it's harder to hold that conversation about making the party a winner at the national level," said former Senate Republican staffer John Ullyot.
Republicans' talk of finding a winning strategy for presidential elections is sometimes drowned out by confident and staunchly conservative lawmakers coasting toward another re-election.
"The age-old conundrum is, do we change who we are to more adequately fit the electoral trends, or do we try to exert the leadership that will change the electoral trends?" said six-term Rep. Trent Franks, R-Ariz. "I am a firm believer in the latter."
Franks said he'd rather see Republicans lose presidential races than "play to the electorate what our polls tell us, regardless of principle."
Rep. Kenny Marchant, R-Texas, said Republicans could risk eroding support if "we make drastic changes in our underlying policies" that led to their House majority.
Immigration is the most pivotal issue in his west Dallas district, Marchant said. While some Republicans outside the South find it easy to endorse comprehensive immigration reform, he said, "almost anything you put out has a second- or third-related cousin, and its name is amnesty."
Republican National Committee Chairman Reince Preibus acknowledges the GOP is "a tale of two parties."