Davidson's Crenshaw joke occurred during the comedian's appearance on "Weekend Update".
NRCC spokesperson, Jack Pandol, released a statement Sunday, criticizing Davidson's actions, adding that being dumped is "no excuse for lashing out" at a war hero.
Davidson cracked a joke about the eyepatch former Navy SEAL Dan Crenshaw wears, likening the Texas Republican's appearance to "a hitman in a porno movie".
Some Twitter users blew up with sharp criticism of Davidson, saying that a veteran's war wound was not an appropriate subject for humor and that Crenshaw deserved an apology.
After multiple surgeries, Crenshaw regained sight in his remaining eye, and deployed overseas two more times.
Davidson received a much harsher response from the National Republican Congressional Committee, which demanded an apology.
He lost his right eye when he was hit by an IED blast in Helmand province in 2012 during his third deployment, according to his campaign website.
For his part, Crenshaw has taken the high road, refusing to demand an apology though admitting that SNL should probably apologize.
"Well, how do you know?" he asked Camerota. And here's the real atrocity in all of this: It wasn't even amusing. "Right? It was not original, it was not amusing, it was just mean-spirited and that's how I feel about it", Crenshaw told TMZ, according to Fox News. "I look like I make vape juice in a bathtub", he said.