Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.) is facing a tough reelection bid while fighting unfavorable ratings, according to a new poll.

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The survey from the left-leaning Public Policy Polling (PPP) released Tuesday found that McCain leads the Republican primary field with 39 percent, followed by former state Sen. Kelli Ward, who has 26 percent. The other three GOP candidates are polling in the single digits.

But in a hypothetical head-to-head match-up, McCain ties Ward with 41 percent.

The incumbent GOP senator also has an unfavorable rating among Republican primary voters, pollsters found, with 35 percent viewing him favorably and 50 percent giving him an unfavorable rating. He fares worse among those who describe themselves as “very conservative.”

If McCain wins the primary, his prospects in the general election are far from certain. He leads Rep. Ann Kirkpatrick Ann KirkpatrickArizona Rep. Tom O'Halleran wins Democratic primary Arizona Rep. Ann Kirkpatrick wins Democratic primary Cook shifts 20 House districts toward Democrats MORE (D-Ariz.) by 6 points, 42 to 36 percent, but has a similar unfavorable rating among all Arizona state voters.

If Ward wins the GOP nomination, however, the general election race is even tighter. She leads Kirkpatrick, 37 to 35 percent.

“John McCain’s going to have a hard time getting through the Republican primary,” Dean Debnam, president of Public Policy Polling, said in a statement. “Even if he does survive Kelli Ward, the general election’s likely to be tough for him too.”

McCain's campaign brushed off the poll's results and said the findings show he's in a better position than when the last survey was conducted.

"We put zero stock in a partisan Democrat poll that is obviously aimed at boosting John McCain’s opponents in the primary and general elections," spokeswoman Lorna Romero said. "And even if you took this bogus poll at face value, it actually shows McCain in a stronger position today than PPP’s last poll, with his favorability up eight points since March."

“John McCain has always known this will be a tight race - that’s why he’s built a strong campaign that’s ready for any challenge this November," she added.

The GOP senator conceded in leaked audio that “this might be the race of my life” with presumptive GOP presidential nominee Donald Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE as the party's standard-bearer. While he said he’d support the eventual nominee, McCain has criticized Trump's harsh rhetoric and called on the billionaire to apologize to prisoners of war.

The PPP poll of 896 registered voters and 443 GOP primary voters was conducted between May 13 and 15. It has a margin of error of 3.3 percentage points for all voters and a margin of error of 4.7 points for Republican respondents.