Glasgow, Missouri (CNN) On a recent tour of a mid-Missouri manufacturer, state Attorney General Josh Hawley was eager to talk about job creation and vocational training, the themes underpinning his visit. And the Republican Senate candidate was especially keen to discuss Democratic Sen. Claire McCaskill, whom he hopes to unseat come November.

But he was far less enthusiastic over speaking about the drama around Missouri Gov. Eric Greitens, in which Hawley, as the state's top lawyer, has grudgingly landed a starring role.

Which is to say, Hawley would not utter the name "Greitens" at all.

"I can't worry about all of the noise and all of those things," Hawley said vaguely, skirting one of a series of questions about how the governor's issues are coming to bear on the Senate race. "And also, it never does any good to say 'woe is me' about any of this stuff."

If Hawley has sought to block out the Greitens noise, however, it is only growing louder. What began in January as a sex scandal has expanded to campaign finance questions, with Greitens facing a felony charge relating to his campaign's use of a nonprofit donor list. Missouri lawmakers are considering impeaching him, with a vote expected early next month.

On Friday, a special Missouri House committee issued a subpoena for Greitens to testify on June 4.

Hawley and a roster of other Republicans have called on the governor to resign, which might have offered a relatively tidy resolution. But Greitens has insisted he will remain in office and fight, likely prolonging the saga at least through the summer, and perhaps into the prime campaign season in the fall.

Whether Greitens' career ultimately survives, Republicans are increasingly concerned that the firestorm around him could also engulf Hawley in one of the crucial Senate races this year, with the balance of power in Washington at stake.

"I think we'd be fooling ourselves a little bit if we didn't admit that Eric Greitens is now intentionally making it more difficult for us to maintain control of the US Senate," said Gregg Keller, a longtime Missouri Republican operative who has been a vocal critic of the governor.

The most visible sign of Greitens' impact on the race thus far has been in millions of dollars' worth of advertising in Missouri by national Democrats' Senate Majority PAC, linking Hawley to the embattled governor. This week the group unveiled its latest ad, which invokes "a governor under fire" and "a capital awash in corruption."

"In the middle, Attorney General Josh Hawley," the ad's narrator says.

Senate Majority PAC has dropped seven figures to air the latest spot, the group's third thus far to highlight Greitens.

Democrats believe the association is beneficial because Hawley will campaign as an outsider who can fix Washington and the Greitens controversy offers a counterpoint.

"It's a perfect distillation of how Josh Hawley is just a regular politician," said Chris Hayden, a spokesperson for the group.

Democrats also hope the issue will stain Hawley's record as attorney general, which his allies anticipate as a major selling point. McCaskill herself has engaged on this angle, telling The New York Times last month, "There is one thing that is very clear: Josh Hawley ran for office saying he was going to clean up public corruption. So far, he whiffed."

Hawley calls the charge "nonsense."

"You can say a lot of things about me, but that I'm not a tough prosecutor is just ridiculous," he said.

Faced with the Greitens dilemma, Hawley has indeed opted to take an aggressive stance, opening an investigation earlier this year into the governor's use of the nonprofit donor list, which led to the felony charge, and calling on Greitens to step down. Greitens' attorneys went so far as to file for a restraining order against Hawley's investigation, suggesting in court that it was motivated by his Senate campaign; but a judge dismissed it.

McCaskill, who hails from a state that favored President Donald Trump by nearly 20 points over Hillary Clinton, is widely considered one of the most vulnerable Democrats in the country. But she's been here before. She also faced steep odds in 2012 -- until her Republican opponent, Todd Akin, famously claimed that rape victims could not become pregnant in the event of a "legitimate rape," because "the female body has ways to try to shut the whole thing down."

Now the cloud over Greitens has some Republicans worried that lightning might strike twice.

"I don't know what good luck charm (McCaskill) carries around," said Missouri state Rep. Kathie Conway, a Republican who represents a suburban area near St. Louis, "but it's potent."

Former Sen. Jim Talent, a Republican who lost his seat to McCaskill in 2006, said he believes Hawley's involvement in the Greitens investigation could help him in one respect, potentially bolstering his reputation among voters "as a straight-shooting guy who does his duty without fear and does it well."

"He hasn't tried to make political hay out of it, he's just done his job," said Talent. "I think that supported his brand."

But Hawley's approach has also risked alienating some Republicans who continue to support the governor and believe the investigations into his conduct are part of a plot by his political enemies to remove him from office.

"A lot of people think (Hawley) is a hero, a person showing a lot of integrity and courage to take on the governor of his own party," said Conway. "Others think he's a turncoat and a RINO," shorthand for "a Republican in name only."

Hawley told CNN he believes "the politics of it shift by the hour, so I don't worry about the politics of it, the political ramifications. I do my job."

The controversy surrounding Greitens has also complicated Hawley's job as a candidate, however, opening up the possibility of awkward questions or run-ins at events, and shifting the conversation away from the would-be core messages of his campaign.

"It tends to suck the oxygen out of other issues that he'd probably like to drive against Sen. McCaskill," said Talent. "It's taken him into an issue matrix that he probably did not anticipate going into."

But Hawley's team remains optimistic, pointing to polling that has shown McCaskill and Hawley neck-and-neck, in addition to McCaskill's status as a Democrat in a state that has trended increasingly red.

"Claire McCaskill's re-election chances are no better than they were last spring, and it's because she hasn't changed the way she votes," said Brad Todd, who is advising Hawley's campaign. "Everything else is just a sideshow."