"They're in a good spot with the electorate, high points in terms of voter support for Republican candidates and elected officials," said Quin Monson, director of the Center for the Study of Elections and Democracy at Brigham Young University.
Going forward, he said the party will have to make a stronger appeal to Latino voters who will make up a growing portion of the electorate.
"The other [challenge], I think, is to stem some of the infighting that has the potential to erupt," Monson said.
A group of longtime Republicans, including former Gov. Mike Leavitt, has formed the group Count My Vote and is considering a ballot initiative to change the state nominating process.
The current system, they argue, puts too much power in the hands of delegates elected at neighborhood meetings who they say don't represent mainstream Utahns.
The initiative and the GOP's struggle over reforms to the state's unique caucus and convention system are expected to be pivotal issues in the race for chairman.
Evans, who served as Salt Lake County GOP chairman from 2005 to 2009 and owns Checkline, a payday lending company, said experience is a key in the party leadership post.
"I think it's fair to state I'd be best positioned to navigate us through the caucus [initiative] issue, and the real reason I decided to run is because we just cannot lose the caucus-convention system," Evans said. "It has served Utah well over the years, but I think everyone agrees we have to update our system."
Gabrielson, a project manager at Redmond Inc., in Heber City, is in his second term as chairman of the Wasatch County Republican Party and says he believes the caucus and convention system is worth defending.
"Let's look at the results. I happen to think we have gotten great results from our neighborhood elections," said Gabrielson. "It's very risky and very dangerous to start mucking around with our nominating system."
Diaz is the CEO of Pantheon Construction and was recently re-elected chairman of the Utah Republican Hispanic Assembly and has been active in immigration reform issues.
"Overall we have a good and solid convention system," Diaz said. "My focus will be to make a good party better. I think we need to change the tone of our party and make it a broader and more welcoming party."
Diaz did not endorse specific changes but said he wants to make it easier for people to participate in the selection of Republican candidates.
Dan Harrie contributed to this report.