The next test will come Saturday, when Wright presents a package of reform proposals to the State Central Committee, the policy-making body for the party.
A group calling itself Count My Vote, concerned that Utah's one-of-a-kind caucus and convention system puts too much power in the hands of a small number of delegates, is considering an effort to give candidates a way around the caucus process.
The group organized by former governor and U.S. Health and Human Services Secretary Mike Leavitt, his former chief of staff Rich McKeown, and others envisions a system where a candidate from either party could gather enough signatures to make it to the primary ballot, and potentially win the party's nomination without the endorsement of the delegates.
But to change the system, they would have to run a costly and labor-intensive initiative drive and put the reforms on the 2014 ballot.
That may not be necessary, however, if Wright can sell the Republican State Central Committee a series of reforms to the caucus system that would satisfy leaders of Count My Vote.
LaVarr Webb, a long-time Leavitt aide who is working with Count My Vote, said leaders are still working out exactly what changes the party would have to make before they would decide not to run their initiative.
"We are formulating and putting in final form the list of things we'd really like to see," Webb said.
Wright said the proposed changes that will be put before the State Central Committee on Saturday are aimed at addressing all of the concerns that Count My Vote leaders expressed.
"I'm hoping those reasonable, common sense solutions will be enough for them," he said.
Don Guymon, a central committee member from Davis County, said he is willing to support changes to make the system more inclusive. But if they undermine the Republican Party, he said, he can't support them, even with the threat of the initiative.
"I see this as some people trying to gain some influence in the party to try to influence elections in their favor," he said. "I'm not going to make drastic changes just because someone is making a threat."
Reforms • One of the key reforms would be requiring candidates to get at least 70 percent of the vote from delegates at convention up from the current threshold of 60 percent in order clinch the party's nomination without going to a primary. That would mean more party primaries giving more voters a chance to participate.
That proposal may be a tough sell for the central committee, however. Last month, about half the members supported raising the threshold, but it requires two-thirds for the committee to make the change, which would still have to be ratified by delegates at the state convention in May.
Webb said his group is also encouraged by some of the changes being discussed about letting people vote for delegates at their caucuses through absentee or early voting.
"It still means … a relatively small number of people at the convention are making these important decisions about who the nominees will be," Webb said. "But if you combine that with the higher threshold, more people get into a primary and the voters in general have a bigger say who the nominee is."
Webb said the group also wants assurances that the party won't reverse course and change the rules back next year. That could mean putting the reforms into state law.
Wright said he feels all of the proposals improve the current system and expand participation, or else they wouldn't even be considered.
"A lot of people don't like the timing and we're doing this with a gun to our head and I can agree with that," Wright said. "But if they're good ideas and increase participation, then they're good in the long run."
Opposition • Wright is concerned he has to contend with opposition being fueled, at least in part, by local representatives of FreedomWorks, a Washington, D.C.,- based group that campaigned aggressively against Sen. Bob Bennett and Sen. Orrin Hatch helping to defeat Bennett because they were not conservative enough.
"It does concern me that I hear from different people that there are outside groups from Washington, D.C., in Utah lobbying members of the State Central Committee to do what is best for them in Washington, D.C.," he said. "Why would [they] not want more people to participate? And the only explanation is you have more control by having fewer people participate."
But Heather Williamson, the Utah director for FreedomWorks, said there is no effort from Washington. Rather, she said she is responding to what she hears from the FreedomWorks members in Utah.
"In Utah, I've heard overwhelmingly from our membership base here that they support the current caucus system and don't want to see the integrity of the current system lost," she said.
Utah Democratic Party Chairman Jim Dabakis said the caucus reform fight is a Republican civil war, and Democrats are staying out of it.
"Helping this plot by this group of Republican moderates who are trying to steal back power, Democrats ought to stay away," he said. "They're there because they feel like they've lost power to the tea party, so they're going to change the rules of the game."
That said, Dabakis said Democrats will also have a committee look at potential changes to its nominating system.
If Count My Vote moves ahead with an initiative drive, the changes would affect all political parties in the state.