This dynamic played out notably in the special Senate election in Alabama late last year, when Roy Moore toppled an establishment rival in the GOP primary despite a long history of controversial views. Moore fell just short of victory in the general election after multiple accusations of sexual misconduct with teenage girls.

Arpaio, who lost his 2016 re-election bid as sheriff and faced jail time for a criminal contempt conviction until Trump pardoned him, wouldn't seem the most viable candidate to replace retiring Republican Sen. Jeff Flake. But like Moore in Alabama, Arpaio has achieved folklore status among many conservative voters. He has never lost a GOP primary in Maricopa County, where approximately 60 percent of the state's electorate resides. And his muscular crackdown on immigration has made him a prodigious national fundraiser: He pulled in a $12.8 million in his losing sheriff's contest.

To be sure, plenty of Republicans are worried that if Arpaio is the party's standard-bearer going into November, voters will reject his incendiary history and views and elect a Democrat. In 2016, despite there being more registered Republicans than Democrats in Maricopa County and Trump winning the county by 3 percentage points, Arpaio lost by 13 points.

"It was Republicans (in 2016) who decided that they had enough of Joe Arpaio, and while he'd excite a certain part of the electorate, he'd turn off a larger portion (in the general election)," said Barrett Marson, an Arizona GOP consultant who is not involved in the Senate contest. "Everybody knows who he is, and it'll be hard for him to define himself as anything different."

A jolt to the Senate race

Arpaio, who as sheriff had made a tradition of riding atop a tank in Phoenix’s annual Christmas parade, made a similarly blunt entrance by jumping into the Senate race in January, just four months after Trump pardoned him.

The president hailed Arpaio as "a patriot" who is "very strong on borders, very strong on illegal immigration." But Trump has yet to endorse his Senate candidacy.

Republicans had anticipated a two-candidate contest for the nomination to replace Flake: Rep. Martha McSally, a retired Air Force fighter pilot, and Kelli Ward, a former family physician and state senator who challenged Sen. John McCain in the 2016 Senate primary (she lost by 12 points but drew national headlines with her suggestion that McCain was too old to serve effectively).

But then Arpaio added a jolt of uncertainty to the now three-way contest.

Arpaio told NBC News his candidacy is serious. But he has yet to hold a campaign event, acquire campaign signs or buttons, or hire any staff outside of his longtime political consultant.

He said he didn't know how much money he had raised for the campaign thus far. (Campaign finance reports have yet to be filed so the information is not publicly available.)

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And he shows little understanding of policy. Pressed for his views on health care, trade and tax reform, Arpaio batted them away as "technical questions."

"When you're asking me now, don't forget: I just made a decision to run," he said in an interview in late January. "Instead of looking at the sports page, I've got to start looking at the newspaper. I don't have the luxury of being in Washington, having all these bills, talking to my colleagues. I'm just the outside guy."

When it comes to the issues, Arpaio said: "The president is always right. I'm going to support the president's agenda."

Tough stance on immigration

Immigration, the issue that catapulted Arpaio to national prominence, remains the topic that animates him most.

As sheriff, Arpaio prided himself on housing inmates, including many Hispanics, in "Tent City," a makeshift jail where thousands were packed into Korean War-era tents for misdemeanor crimes like driving under the influence. There they were forced to endure the swings in the desert climate — often freezing at night, triple digits by day — wearing black-and-white striped jumpsuits and pink underwear.