Sheriff Joe appears to be out of money and out of time. As Arizona Republicans head to the polls next week to pick their nominee for their state’s open U.S. Senate seat, former Maricopa County chief lawman Joe Arpaio is stumbling in his attempt for a political redemption comeback.

Not only is he struggling in the polls, but he’s also far behind in the all-important fundraising race — a real surprise to observers who’d seen him collect $12 million just two years ago in his losing bid for a seventh term as sheriff.

Instead the main question appears to be how much of the conservative vote he’ll draw in a losing effort, and whether he’ll end up playing the role of spoiler in the two-woman race between Rep. Martha McSally and former state Sen. Kelli Ward.

“If Sheriff Joe was not in the race Kelli Ward would beat Martha McSally by 20 points,” said Eric Beach, the strategist for Ms. Ward.

Some conservatives have suggested Mr. Arpaio drop out in order to clear a path for Ms. Ward. They fear Ms. McSally won’t be a staunch enough supporter of President Trump if she reaches the Senate.

Looking to defuse those complaints, the congresswoman has moved to embrace Mr. Trump during the campaign, attending White House events and basking in presidential shout-outs. She’s also downplayed past support for illegal immigrant “Dreamers” and instead focusing on a get-tough approach to the border and interior enforcement.

That may have been enough to earn Mr. Trump’s continued silence in a race where his endorsement could mean certain victory for whomever he blessed.

Last year, when Sen. Jeff Flake, a Republican, was still expected to run for re-election to the seat, Mr. Trump appeared to back Ms. Ward, saying he was happy to see her challenge Mr. Flake, perhaps the most vocal critic of the president among Senate Republicans.

But when Mr. Flake announced his retirement the race opened up.

Mr. Arpaio, who lost his bid for a seventh term as Maricopa County sheriff in 2016, jumped into the Senate contest in early January, counting on deep ties to Mr. Trump, whom he backed during the 2016 campaign.

The president repaid the former sheriff by pardoning him last year for his criminal contempt of court conviction — a move that still irks Democrats and some liberal legal scholars.

Ms. McSally announced her own bid soon after Mr. Arpaio, encouraged by establishment Republicans who believed she was the best chance to keep the seat in GOP hands in a battle against Democratic Rep. Kyrsten Sinema, who faces nominal opposition in her party’s primary.

If Republicans hold the seat in November, they are confident they’ll keep control of the Senate. If they lose it, that control is in significant jeopardy.

Thomas J. Volgy, a political scientist at the University of Arizona, said it should have been clear from the start that Mr. Arpaio wouldn’t survive the primary.

He said the former sheriff was too damaged by his 2016 loss and the legal troubles he that helped contribute to it — including the criminal contempt of court finding by a judge who ruled his department continued to target Hispanics for enforcement even after being ordered by the courts to stop.

“I have no idea why he thought, or anyone else supporting him thought, he could win that primary. That was a failing race from the beginning,” Mr. Volgy said. “In 2016 he got a lot of support from people who were far to the right and I think he got it nationally. Once he lost that race and once he fell in legal trouble it became a whole new ball game. Arizona is just not the place where you’re going to support a guy who was on his way to jail for racial profiling.”

When Mr. Arpaio entered the race, his Republican opponents had feared he would swamp them with cash. They’d seen his sheriff’s race in 2016, when he collected more than $12 million, tapping a national network of donors he built over the years based on his billing as America’s toughest sheriff.

The money just never materialized this time.

As of two weeks ago he’d raised just $1.3 million, and in the weeks from July 1 to Aug. 8 collected just $182,028.

Ms. Ward collected $410,460 over that same time, and $3.1 million over the course of the campaign. And Ms. McSally led the pack with $1 million in the July 1 to Aug. period, and $6.1 million during the course of her Senate bid. That’s in addition to $1.6 million she shifted over from her House campaign.

Ms. McSally also leads in the most recent polling. A Data Orbital survey released Thursday put her at 48 percent to Ms. Ward’s 22 percent and Mr. Arpaio’s 18 percent. An OH Predictive Insights poll last week also gave her Ms. McSally a massive lead of 47 percent to Ms. Ward’s 27 percent. Mr. Arpaio had just 13 percent of the vote in that poll.

Mike Noble, the chief pollster at OH Predictive Insights, said voters who’d been undecided in July appear to have stormed to Ms. McSally as Ms. Ward and Mr. Arpaio started firing at each other.

“They kind of broke each other, and McSally’s taking it away,” he said.

One complication for the candidates is that more than half of voters cast ballots early, and the deadline for those ballots was Wednesday. That means a large chunk of the primary vote is already locked in, and Mr. Noble said if that is reflected in votes for McSally, it will be very difficult for Ms. Ward to overcome that on Election Day.

“It becomes a very tough math problem,” he said.

Ms. Ward’s campaign questions the latest polling, and points back to a two-month-old survey by NBC/Marist showing Ms. McSally up by just 2 percentage points. Mr. Beach, the Ward strategist who’s also chairman of a pro-Trump political organization, Great America, said they believe Ms. Ward trails by between 3 and 6 points.

The path to victory, he said, depends on what voters do with Mr. Arpaio. If voters on the right remain split, Ms. McSally will win. But if conservative voters ditch Mr. Arpaio and back Ms. Ward, she’ll emerge the party’s nominee, he said.

“We believe that Kelli is the only solid conservative, we believe it’s a two-way race, but Joe’s participation in the race does dilute the conservative vote, which is unfortunate,” Mr. Beach said.

Mr. Arpaio’s campaign offered several times to arrange an interview between the former sheriff and The Washington Times, but didn’t follow through.

On the campaign trail, though, Mr. Arpaio bristles at the suggestion he’s playing spoiler to give Ms. McSally an assist.

“I’m not convinced that Martha won’t work with the Deep State, the Democrats, and the Fake News and vote to impeach President Trump if she’s elected and I’m insulted that anybody would insinuate that I would be associated with her in any way,” he said in a press release this week.

For her part Ms. McSally is already looking past the primary.

Her campaign on Thursday announced a new ad highlighting her own history as an Air Force combat pilot, contrasting that with Ms. Sinema, showing footage of the presumptive Democratic nominee in a pink tutu during a 2003 anti-war rally.

Ms. McSally, in the ad, says Ms. Sinema was “denigrating our service.

“The world is a dangerous place. We need strong leaders who understand the threat, and respect our troops. Kyrsten Sinema fails the test,” the Republican congresswoman says.

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