DES MOINES, Iowa — In the days since Republicans lost an election many in the party thought was theirs, chatter has been bubbling about what the GOP should do to recover.

For Iowa Gov. Terry Branstad, it starts with the smallest of actions: abandoning the state’s now-infamous straw poll.

Once a festive checkpoint on the road to the leadoff Iowa caucuses, the poll has devolved into a full-blown sideshow, Branstad and other critics contend. They say it’s an unfair and false test that has felled good candidates and kept others from competing in the state.

“It’s just something that’s gotten totally out of control,” said veteran GOP presidential campaign consultant Charlie Black. “It’s been bad for years, but no one has had the guts to say it until now.”

The poll, which morphed over the decades into a closely watched early test of caucus campaign strength, had “outlived its usefulness,” Branstad told The Wall Street Journal this week. Some activists contend it amplifies the voices of candidates lacking broad appeal.

Branstad says he has widespread support for a different event to replace the poll, held in Ames the summer before every contested presidential caucus since 1979. It has become a lavish affair where campaigns spend heavily to wine, dine, entertain and chauffeur their supporters by bus to the Iowa State University campus.

Critics have increasingly called it a shakedown. Not only do campaigns buy up thousands of tickets for their supporters to attend the event, they bid thousands of dollars for prime spots to pitch tents near the voting area on the college campus.

It’s all to show early support in Iowa, where the precinct caucuses traditionally lead off the early-state nominating march, even though only a fraction of caucusgoers turn out for the straw poll.

“It’s a tedious effort. It costs a lot of money. It’s totally irrelevant at the end of the day. It used to be a test of organization,” said Ed Rollins, who managed Minnesota Rep. Michele Bachmann’s presidential campaign at the time she won the 2012 straw poll. “Today it’s a lot of effort and a lot of energy that really is not worth the effort.”

Bachmann spent $2 million on the August straw poll and edged Texas Rep. Ron Paul with heavy support from religious conservatives.

“The straw poll doesn’t provide a complete cross-section of the caucus-going electorate,” said Phil Musser, an adviser to former Minnesota Gov. Tim Pawlenty.

Pawlenty pinned his hopes on a strong finish in Ames last year but dropped out of the race for the GOP nomination after finishing third, never reaching the caucuses in his neighboring state.

Only about 17,000 turned out for the straw poll, one-seventh the size of the roughly 120,000 who voted on caucus night in January.

John McCain, the GOP’s nominee in 2008, and onetime favorite Rudy Giuliani opted not to compete for the straw poll, turned off by the event’s heavy influence by Christian conservatives. They ran scaled down caucus campaigns as a result.

Romney did not compete in the 2011 straw poll, choosing to project himself as a national candidate who didn’t need to define himself among the Iowa GOP’s rank and file.

But in 2007, Romney spent millions and won, only to struggle to a second-place caucus finish. A month later, he quit the race.

During that campaign, the former Massachusetts governor was so struck by the ferocity of opposition by Iowa Republican activists to illegal immigration that he tacked to the right to distinguish himself from Giuliani and McCain, who supported relaxed sanctions for illegal immigrants.

Doug Gross, a leading Iowa Republican who chaired Romney’s 2008 Iowa campaign, said Romney’s strong opposition to any pathway to citizenship or tuition benefits for illegal immigrants hurt him in the general election four years later against Obama, partly due to his effort to appeal to Iowa conservatives at the straw poll.

The straw poll “forces them to deal with extremists and you can’t help but have some of that rub off on you,” Gross said. “That hurts our ability to nominate candidates who can win.”

Advocates of the straw poll argue the money helps finance the caucuses, which are party-run, not state-run, elections.

Instead, Branstad’s allies are urging the party to substitute the straw poll with a summer fundraiser, without a vote.

Without the straw poll, the caucuses may lure back all top-tier Republican contenders, Branstad’s supporters say. That would raise the stakes for the caucuses by making them truly the first event to winnow the field.

“(The straw poll) was great in its time,” said Iowa GOP strategist John Stineman. “It’s time to move on.”