The state's convention is notoriously volatile — convention delegates ousted longtime Sen. Bob Bennett (R-Utah) two years ago for having an insufficiently conservative voting record. But Hatch recognized the threat early and worked hard to make sure that his supporters turned out in large numbers for the party's caucuses, which occurred a few weeks ago and determined who gets to attend the convention. In the poll, just one-fifth of this year's convention-goers attended the 2010 convention that ousted Bennett.

FreedomWorks, a national group that backs Tea Party candidates, spent more than $600,000 targeting Hatch, a longtime senator. A FreedomWorks spokesman told The Hill last week that while they were still tabulating their own convention poll, they were convinced Hatch would still be vulnerable for defeat at the convention. But Hatch's internal poll, showing him well ahead of his GOP rivals, suggests they're wrong.

The poll was conducted of 335 delegates, nearly 10 percent of the 4,000 who will attend the convention.