McConnell, who faces re-election in 2014, is married to Elaine Chao, a former labor secretary under President George W. Bush. Last week, a group called Progress Kentucky sent out a series of tweets, calling attention to McConnell's wife, one saying, "May explain why your job moved to #China!"
"Her family escaped from the Communists in mainland China, made their way to America and have lived the American dream," McConnell said on CNN's "State of the Union" Sunday. "And for that [she faces] racial slurs by the Democrats in Kentucky. It sort of goes with the turf at home."
Progress Kentucky apologized for the tweets. The group's director Shawn Reilly said a spokesman for the group has stepped down and the volunteer who wrote the tweets is no longer affiliated with Progress Kentucky.
"Those tweets did not reflect our values, and we are committed to making sure nothing like that happens again," Reilly said in a statement. "Our key goal is to elevate the conversation about Senator McConnell's record and the kind of representation Kentucky deserves. We didn't advance that goal with a few of our tweets. We pledge to do better in the future."
McConnell wasn't the only one training fire on Progress Kentucky. Actress and activist Ashley Judd -- a Kentucky native who has been rumored to be considering challenging McConnell next year -- said she found the remarks on Twitter offensive.
"Whatever the intention, whatever the venue, whomever the person, attacks or comments on anyone's ethnicity are wrong & patently unacceptable," she wrote Wednesday on Twitter.