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The group is waiting for the outcome of the convention before deciding how to approach a possible two-candidate primary.

“We’ll do our own poll after the convention, and if we think he’s beatable, we’ll stay in the race,” Mr. Walker said. “If we don’t think he’s beatable, we’ll back out of the race.”

One wild card that probably helped Mr. Hatch this year was the Church of Jesus Christ of Latter-day Saints. The church encouraged its members to attend the March party caucuses, which resulted in roughly double the turnout at the Republican caucus.

The result was a delegate group that was somewhat less conservative and less politically active than the pool that emerged from the 2010 caucus, which was dominated by Tea Party activists.

“You had a lot of people from the caucuses who really only knew Orrin Hatch,” Mr. Walker said. “They’re basically conservative, but they really didn’t know a lot of the issues surrounding this election.”