One of the quirkiest rituals of the presidential election—the straw poll of Republican voters in Ames, Iowa—is obsolete and should be eliminated, Iowa's GOP governor says.

"I think the straw poll has outlived its usefulness," Gov. Terry Branstad said in an interview about the political jamboree. "It has been a great fundraiser for the party, but I think its days are over."

The governor cited the results of the most recent Ames Straw Poll as evidence for why the event should be spiked: Rep. Michele Bachmann won in 2011, only to fizzle as a candidate soon after. The comments immediately touched off controversy among Republicans in Iowa, the leadoff state on the presidential primary calendar.

Going back to 1979, Republican presidential contenders have flocked to Ames in August to eat fried food, dance to country bands and wheedle votes from the party faithful in what is billed as a trial run for the real Iowa caucuses early the next year, but which also serves as a fundraiser for the party.

Its track record as an anointer of GOP nominees falls far shy of impressive. Only two victors, Bob Dole in 1995 and George W. Bush in 1999, went on to win the Iowa caucus the following year and then the nomination in November. And only one straw-poll winner, Mr. Bush, went on to become president.