JEFFERSON CITY, Mo. — It didn't take long after Missouri Gov. Eric Greitens was indicted for alleged invasion of privacy for Missouri Democrats to tie him to Attorney General Josh Hawley, the presumed GOP front runner in Missouri's hotly contested U.S. Senate race.

Nor did it take long for Republicans to link the prosecutor who announced the charges to a prominent national Democratic financier.

The quick injection of politics was a strong sign that Greitens' potentially prolonged legal battle stemming from an extramarital affair could have implications for the 2018 elections — especially for fellow Republicans whom history suggests have a disadvantage as the party in power during the midterm of Donald Trump's presidency.

Related: Missouri governor indicted on invasion of privacy charge related to affair

So far, Greitens, 43, has remained defiant against growing but not-yet-overwhelming calls to resign from some fellow Republicans, while instead portraying the felony charge against him as nothing more than a political jab by a "reckless liberal prosecutor."

The Missouri Republican Party noted that St. Louis circuit attorney Kim Gardner had received more than $200,000 from wealthy liberal financier George Soros during her campaign — casting the indictment as part of a broader Democratic attack on Republicans.

The Thursday indictment came just five days ahead of Tuesday's start of the candidacy filing period for Missouri residents wanting to run for U.S. Senate, Congress, and state and local offices. Hawley is challenging Missouri Democratic Sen. Claire McCaskill.

An incumbent governor typically is a help to his party in races such as the Senate, but an indicted one could be a detriment.

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"It doesn't help the image of the Republican Party, so in that sense it helps McCaskill and hurts Hawley" in the Senate race, said Ken Warren, a longtime political scientist at Saint Louis University.

The Missouri Senate race is being closely watched as one that could determine control of the chamber, where Republicans now have a bare majority of 51 seats. McCaskill is one of only two statewide-elected Democrats in Missouri, which Donald Trump carried by nearly 20 percentage points in 2016. Republicans got behind Hawley early after a disastrous 2012 campaign when McCaskill defeated Todd Akin following his comments about "legitimate rape."

Whether Democrats can effectively tie Greitens to Hawley remains to be seen. But indications are that they will try.

Missouri Gov. Eric Greitens outlines his tax overhaul plan to supporters at Doyle Manufacturing on Jan. 29, 2018, in Palmyra, Mo. Jeff Roberson / AP file

On Friday, The Missouri Democratic Party noted that Hawley had accepted nearly $50,000 in contributions from Greitens in 2016 and has not called on Greitens to resign. The attorney general is conducting an investigation over Greitens' use of a secretive app that deletes messages once they've been read. It's unclear when the investigation will conclude.

Hawley took to Twitter on Friday and, without mentioning Greitens, noted that an indictment "is a serious matter" with no place for partisanship. He also expressed support for a newly announced legislative investigation into the governor, saying he's confident "the House's investigation will be thorough and swift, and will proceed without regard to party."

That House investigation could serve as a first step for impeachment proceedings against Greitens, though it also could determine he has done nothing warranting his removal from office.

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University of Missouri political science professor Peverill Squire said the 38-year-old Hawley is in a "very awkward" spot.

"As the state's chief legal officer, he has to not appear to question the veracity of the legal process and certainly be supportive of prosecutorial staff," Squire said. "The other problem is, of course, he's sort of the other young and up and coming Republican, and although he obviously doesn't wish to get confused with Greitens, it'll be hard for him to distinguish himself."

McCaskill, a former prosecutor, has not commented about Greitens' indictment, and spokespeople for both her Senate office and campaign did not respond to messages from the Associated Press seeking comment on Friday. But she took a political jab at him after the media reported last month that Greitens had engaged in a 2015 affair with his former hairdresser. The woman was recorded as saying that Greitens had blindfolded her, bound her hands and took an unwanted photo of her during a sexual encounter in the basement of his St. Louis house.

Speaking to Democrats in Columbia, McCaskill quipped last month that Greitens had run as a political outsider.

"He was going to do things that literally no other governor had done," McCaskill said, as reported by the Columbia Daily Tribune. "Little did we know it was sex in the basement."

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Republican consultant John Hancock, who is not affiliated with either Greitens or Hawley's campaign, called the indictment a "political sham" but added that the underlying facts of Greitens' affair pose "a real political problem" for Republicans in the 2018 elections.

In presidential midterm elections, supporters of the incumbent president's party typically are less motivated that those in the challenging party, he said. The president's party typically loses seats in Congress. Hancock said Greitens' troubles could provide yet another reason for Republican voters to stay home on Nov. 6.

"A depressed turnout affects the entire ticket," Hancock said.

Warren said that if Hawley starts to fall behind in the race, Republicans could pressure Greitens to resign. Noting the governor's maverick streak, he doubts it would work.

"Since when has he taken cues from fellow Republicans?" Warren asked.