Republican Senate candidate Rand Paul said Monday that he hasn't yet decided whether or not he wants to appear alongside his Democratic opponent, Jack Conway, after Conway said Paul belonged to a group in college that "mocked Christianity." 

"We haven’t fully decided, but I’m not sure I’ll appear in public with someone who is going to question my religion," Paul told reporters after an event Monday.

In a contentious debate Sunday night, Paul and Conway sparred over the Democrat's latest attack ad in which a narrator asks, "Why did Rand Paul once tie a woman up, tell her to bow down before a false idol… ." 

At least one prominent Democrat has already criticized Conway for the spot. Sen. Claire McCaskill (D-Mo.) said Monday on MSNBC's "Morning Joe" that she thought the ad was "very dangerous." 

A Paul campaign source said the candidate will make a decision soon on the upcoming debate, which is planned for next Monday, but that pulling out of the meeting is a real possibility. 

"This attack really is that personal to him," the source said.  

During Sunday's debate, Paul called Conway a "disgrace" over the attack, and after the debate concluded walked off the stage without acknowledging his Democratic opponent.