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Mr. Pearce’s strategy so far appears to be emphasizing the economy, rather than illegal immigration, his signature issue. After the tea party meeting, he told local reporters that his campaign focus would be “jobs, jobs, jobs.”

“I like Russell Pearce’s chances in a Republican primary,” said Republican political consultant Jason Rose. “I’m already starting to see comments from Pearce — he’s talking about jobs and the economy. Not that he’ll ever shy away from immigration, but he’s reminding people that he’s a Republican for lots of other reasons.”

Targeting the sheriff

In the Maricopa County sheriff’s race, three other candidates — two Democrats and an Independent — have indicated they will challenge Mr. Arpaio, who so far has not drawn a Republican challenger. If the other candidates are able to gather enough signatures to qualify for the ballot by May 31, a crowded race would aid the sheriff by splitting the anti-Arpaio vote.

The anybody-but-Arpaio campaign has responded by trying to cull the field. The National Tequila Party Movement, a women’s political group that calls itself an advocate for “compassion towards immigrants and legal immigration reform,” sent out a blistering press release Monday urging Democrat Paul Penzone, a law enforcement officer, to withdraw, saying he “needs to get out of the race since he will spoil the vote.”

The group endorsed independent candidate and police veteran Mike Stauffer. “Mike Stauffer is the only one who can replace Joe Arpaio and everybody knows that Stauffer filed to run against Arpaio way before Penzone did,” said the group’s press release.

Meanwhile, Mr. Parraz says he favors Mr. Penzone, if only because the Democrat appears to have the necessary resources.

“Penzone is doing well raising money. The other Democrat and independent, not so much,” said Mr. Parraz. “If we all share an interest in getting rid of Arpaio, there’s no sense in having an Independent candidate. What I hope we can do is share information so that he can make a decision and be part of a team.”

Money may be the key factor in defeating Mr. Arpaio, whose national reputation as “America’s toughest sheriff” has helped him raise a massive war chest that tops $4 million. The sheriff has attracted fresh scrutiny recently for his investigation into the validity of President Obama’s birth certificate, but he has also won kudos for his work against animal cruelty, which can be his ace in the hole with unaffiliated voters.

“In the last four years there’s been a lot of turbulence,” said Mr. Rose. “But with $4 [million] to $6 million, that’s a mighty big plane to help you get through it. Other candidates will pick on his deficits, but he’ll have the resources to pummel the deficits of any other candidate.”