U.S. Rep. Chris Cannon is in a fight for his political life, a new poll shows.

Cannon, R-Utah, is neck-and-neck with fellow Republican Jason Chaffetz in the 3rd Congressional District Republican Party primary on June 24, found a survey conducted for the Deseret News and KSL-TV.

Cannon leads Chaffetz 39 percent to 37 percent among 3rd District voters who said they are "very likely" or "somewhat likely" to vote next month, according to a poll conducted by Dan Jones & Associates on May 13-19. Those results are within the poll's margin of error of plus or minus 7 percent. Nineteen percent were undecided.

However, when Jones culled out only Republican likely 3rd District voters, Cannon leads Chaffetz 49-34 percent. Among those who said they usually vote "strong Republican," Cannon leads 44-33, Jones found.

Rep. Jim Matheson, D-Utah, is well ahead of his GOP opponent, Bill Dew, in the 2nd Congressional District, the poll shows. Matheson is up 67-20 percent; 11 percent are undecided.

And GOP Rep. Rob Bishop also holds a commanding lead over his Democrat challenger, Morgan Bowen, in the 1st District. Bishop is ahead 58-19 percent; 19 percent is undecided.

Both Cannon and Chaffetz hold large leads over the Democrat in the 3rd District race, Bennion Spencer. So whomever comes out of the GOP primary would be favored to win. Cannon leads Spencer, 50-19 percent (with some other voters picking other candidates or are "undecided"); while Chaffetz leads Spencer 46-18 percent.

The Utah Republican Party has closed its primary. Only those who are registered Republicans and those who are political independents who are willing to register as a Republican at the polls on primary day can get a Republican ballot.

Registered Democrats can't vote in a GOP primary.

Jones, who has polled in Utah for more than 30 years, found that among Republicans Cannon does better against Chaffetz than he does among the general populace of registered voters — good news for the incumbent.

Cannon, brother of Deseret News editor Joe Cannon, has faced Republican opponents in five of his seven races for the U.S. House. And he's defeated each of them. But earlier this month Chaffetz fell just a few votes short of getting 60 percent of delegate support in the state Republican convention — and thus, eliminating Cannon. Now the two face each other in the GOP primary.

Clearly, Chaffetz would be helped if some independents came into the GOP primary in five weeks to vote for him. And Jones found that 48 percent of the district's independent voters said they favored Chaffetz, only 21 percent liked the incumbent Cannon.