(CNN) The indictment of Missouri Republican Gov. Eric Greitens on a felony charge of invasion of privacy Thursday night further imperils his already dicey political future.

The charge stems from allegations that Greitens used a photo of his naked mistress as a form of blackmail to keep her quiet about their affair. Greitens had acknowledged the affair but denied the blackmail allegation.

In a statement on the indictment, the circuit attorney for St. Louis, Kimberly Gardner, said the alleged incident took place in 2015; she pledged to "hold public officials accountable in the same manner as any other resident."

Greitens' attorney, Edward Dowd Jr., said of the charge : "In forty years of public and private practice, I have never seen anything like this. The charges against my client are baseless and unfounded. My client is absolutely innocent. We will be filing a motion to dismiss."

I'm no lawyer and won't make any predictions about how the legal proceedings will play out. But I know politics -- and I can guarantee you Greitens' chances of surviving this mess just went way down.

Greitens appeared to have weathered the initial furor caused by CNN affiliate KMOV's first report of the affair and the allegations in January. That, in spite of the fact that some of the enemies he had made within his own party used the revelations to even the score with him; he received only tepid support from Republicans in the state Legislature.

"Like many Missourians, we find these serious allegations shocking and concerning," Missouri Senate Republican leaders said in a statement. "As this situation is evolving, we expect the governor to be honest and forthright."

As Jason Rosenbaum of St. Louis Public Radio told me last month of Greitens : "He doesn't have the robust support among elected political leaders to get a lot of backup right now. Railing against 'career politicians' can be an attractive message, but it can also have its downsides when those people have to pass your agenda."

But the dam never really broke on Greitens. For the past month-plus, he disappeared from the national news -- and Republicans in the state weren't forced daily to go on the record either in support or opposition to him.

Then today happened.

It is going to be very, very hard for any Republican in Missouri -- or anywhere else -- to avoid having a position on whether Greitens should stay or go after the indictment.

"We will carefully examine the facts contained in the indictment, and answer the question as to whether or not the governor can lead our state while a felony case moves forward," Missouri House Speaker Todd Richardson, Floor Leader Rob Vescovo and Speaker Pro Tem Elijah Haahr -- all Republicans -- said Thursday in a statement, announcing they have begun an investigation into the matter. "The people of Missouri deserve no less. We will begin the process of tasking a group of legislators to investigate these serious charges."

The Democratic Governors Association called for Greitens to resign late Thursday -- and you can expect plenty more Democrats to follow suit.

Greitens may try to bunker in -- again -- in hopes that this all passes, he is exonerated and he can recover enough to be a credible candidate for a second term in 2020.

But given Missouri's clear Republican lean -- and the seriousness of the charge Greitens is facing -- it's possible that Republicans in the state (and nationally) will decide to cut bait on the incumbent rather than risk badly tarnishing the party's brand.

I might even say that scenario is now probable.