Washington (CNN) Republican Sen. Jeff Flake's retirement Tuesday could actually boost his party's chances of holding onto his seat in Arizona in the 2018 midterm elections.

It's an unusual political reality: Typically, it's harder to beat an incumbent like Flake than to win a race for an open seat. But Flake's position as an antagonist in President Donald Trump's Republican Party had flipped that conventional wisdom on its head.

He was almost certain to lose in a Republican primary to conservative challenger Kelli Ward . Ward, though, is seen by many GOP strategists as a poor candidate in a general election matchup with Democratic Rep. Kyrsten Sinema. With Flake out of the way, Republicans are now free to recruit a potentially stronger candidate into that primary.

Flake acknowledged the odd circumstances Tuesday as he announced he'd quit.

"It's difficult to move forward in a Republican primary if you have been critical of any of the behavior that's gone on," Flake said in an interview with CNN's Jake Tapper an hour after his speech announcing his retirement on the Senate floor.

"Based on the lack of support he has from the people of Arizona, it's probably a good move," White House press secretary Sarah Sanders said

Private polls by GOP and Democratic groups showed his approval ratings in the 20s among Arizona Republican voters. Those polls showed Flake being crushed by Ward, who had already entered the August 2018 primary, in a head-to-head contest.

So Trump's White House had spent months attempting -- without success -- to find someone else to enter the race and challenge Flake. Among the factors hindering potential candidates: the potential for primary votes to be split three ways.

Now that Flake is retiring, finding an alternative to Ward to enter the primary could be a lot easier.

"The one political upshot of Sen. Flake's decision today is that Steve Bannon's hand-picked candidate, conspiracy-theorist Kelli Ward, will not be the Republican nominee for this Senate seat in 2018," said Steven Law, the president of the Senate Leadership Fund, a super PAC that supports Republican candidates and incumbents.

Graham may run, Schweikert won't

Robert Graham, the former Arizona Republican Party chairman, told CNN's Brooke Baldwin on Wednesday that he "now, more than ever" considering entering the race. He said Ward is "blinded by ambition" and lacks policy depth.

Graham had previously told CNN he will travel to Washington next week to meet with political action committees supporting Trump and leading figures in Trump's political orbit.

One potential contender many establishment Republicans hoped would run, Rep. David Schweikert, told reporters Wednesday he isn't interested.

"There's no burn in my heart to run for the Senate," he said.

Schweikert said he was surprised by Tuesday's announcement and thought virtually all Republicans in the delegation could be taking a look at the race, but admitted he didn't know who would jump in. The Arizona congressional delegation is meeting Thursday on Capitol Hill, where the subject is sure to come up -- but Schweikert stressed that such meetings take place regularly.

In Arizona, others are looking to state treasurer Jeff DeWit, who was the Trump campaign's chief operating officer, one Arizona Republican operative said.

"The deal is, DeWit has two days to grab the ring. It's his if he wants it, but he's got to move quick. If he wants it, everyone steps out the way. If he doesn't, chaos ensues," the operative said.

If DeWit runs, he "definitely has the President's support" -- whereas others would have to earn that backing, the operative said.

The operative said Schweikert and Paul Gosar, as well as former congressional candidate and GoDaddy executive Christine Jones, are potential candidates if DeWit doesn't run.

A GOP aide also mentioned Reps. Martha McSally and Andy Biggs and state attorney general Mark Brnovich.

Both conversations took place before Schweikert told reporters Wednesday he won't run.

Looming above it all is uncertainty over Arizona Sen. John McCain, who is battling brain cancer.

What Republicans agreed on was that Flake's retirement undercut the central argument of Ward's candidacy.

"You could officially write the obituary for Kelli Ward's campaign today -- it was nice knowing you. Her best campaign line was, 'I'm not that guy,'" the Arizona Republican operative said.

Flake's retirement is a victory for Trump, who had made clear he wanted the senator out. He told supportive Republicans in Arizona prior to the 2016 election that he would spend $10 million of his own money to see that Flake is unseated in the primary.

His White House has been in regular contact with DeWit, Graham and other Republicans about the race. Bannon backed Ward even while working in the White House, and Robert Mercer, the GOP mega-donor and close Bannon ally, has given $300,000 to a pro-Ward super PAC.

At an August campaign rally in Phoenix, Trump huddled backstage with DeWit, Graham and Franks. Two sources familiar with the meeting told CNN it was focused on ousting Flake -- who Trump calls "the flake."

For his part, Flake refused to endorse Trump in the general election, and then three months ago published a book sharply critical of Trump titled "Conscience of a Conservative: A Rejection of Destructive Politics and a Return to Principle."