In audio obtained by CNN and published this week, Graham is heard saying, "White men who are in male-only clubs are going to do great in my presidency." The South Carolina Republican said he made the comments several weeks back at the Hibernian Society of Charleston, an all-male club.
The senator was also recorded cracking wise about Baptists, saying, "they're the ones who drink and don't admit it." Graham is a Southern Baptist.
Graham is expected to cruise to reelection on Tuesday. He has toyed with the idea of running for president, but isn't generally regarded as a top-tier contender.
Brad Hutto, Graham's Democratic challenger, said in a statement earlier this week that Graham "let his true colors show" in his recorded remarks.