Salt Lake County Councilman David Wilde is also seeking the Republican nomination, but he doesn't fare much better, garnering 20 percent compared to Matheson's 62 percent.

"If it came down to a head-to-head with Matheson, I am confident we would catch up fairly well," said B.J. Forsgren, spokesman for the Wilde campaign. "People haven't had a chance to get to know him yet, and once they do he will bring in the votes."

Jones said the early poll results are an accurate measure of name identification, but not of how the candidates measure up with delegates who will decide the slate of candidates in the May 8 state convention. But name identification is also important to the delegates, who care more about winning in November.

"The delegates want to know which candidate can win in the general election, who will do the best for the party," Jones said.

There is still plenty of time for candidates to score name identification with delegates, and the competition for delegates' attention will intensify before the state convention, Jones said.

If the Republican primary were held today, the poll found that Swallow would win handily with 36 percent, compared to 6 percent for Bridgewater and 3 percent for Wilde. But with 43 percent undecided, the race for the GOP nomination is up for grabs.

Those undecided voters hold the key, Forsgren said. "David (Wilde) has personally met with or talked to every single delegate, and he will do it again before the state convention. He runs a very good grass-roots campaign."

Considering Bridgewater and Swallow were locked in a bitter and much-publicized primary election two years ago, shouldn't they already have name identification with voters?

"People forget immediately. It's amazing how fast they forget," Jones said. "You just have to keep your name in the public."

And even though both Swallow and Bridgewater have been out campaigning and raising money since their 2002 defeats, both have been out of the public eye.

Swallow points to the 30-point advantage he has over the other Republicans to make the argument his candidacy is far ahead in name recognition and that he has the only legitimate chance to beat Matheson.

"Frankly, I don't think you can come back from 40 points down," he said, referring to the deficits faced by Bridgewater and Wilde.

Bridgewater did not return Deseret Morning News phone calls for comment.

Most of the public's attention has been focused on the race for governor, where nine GOP candidates are vying for the nomination and a spot on the ballot opposite Democrat Scott Matheson Jr., Jim's brother.