This post was updated at 5:20 p.m. to reflect the group's tweets about McConnell's sexual orientation.

A Democratic super PAC launched recently to oppose Senate Minority Leader Mitch McConnell's (R-Ky.) reelection is under fire for tweeting about McConnell's "Chinese" wife and suggesting that the senator is gay.

The group, Progress Kentucky, tweeted the following  Feb. 14 about McConnell and his wife, former labor secretary Elaine Chao, who is of Chinese descent and was born in Taiwan:

From WFPL public radio:

The Tweet links to a Web site run by conspiracy theorist and radio host Jeff Rense, alleging Chao, who was born in Taiwan, discriminated against American workers during her tenure.

Progress Kentucky spokesman Curtis Morrison says the group's leaders do not review every Tweet and initially denied any had mentioned Chao superficially. But he later told WFPL that a group volunteer had sent out the messages targeting the former secretary.

"It’s not an official statement. It’s a Tweet. And we will remove it if it’s wrong," he says. "I follow Ashley Judd on Twitter and she removed a Tweet the other day, she Tweeted to you, Phillip. People make mistakes in Tweets. It happens. Inferring that Elaine Chao is not a U.S. citizen was not our intention."

Many of the group's tweets have attempted to link McConnell to outsourcing to China and several have referenced Chao and her past comments.

The group even re-tweeted someone's suggestion that McConnell made Chao's father rich and gave her citizenship:

The group told the WFPL reporter that it will take down tweets deemed to be offensive, but it had not done so as of this posting.

"It's a fine line, and that is not our overall message. We’ve got some Tweets there that shouldn’t be there and I’ll make sure they come down. We don’t want to cross that line," Morrison told the reporter. "We’re not after anybody because they are an immigrant, but I think it’s fair to question whether or not there’s a conflict of interest."

Later Tuesday afternoon, BuzzFeed reported that the super PAC's Twitter account had also tweeted twice suggesting that McConnell was gay and linking to an old news release written by an activist who has made similar accusations against several other politicians.

"Is @mcconnellpress a gay-bashing gay senator?" asked one of the tweets, both of which have been deleted.

Republicans called on the Democratic establishment to repudiate the group.

"This is disgusting and must be condemned immediately by top Democrats across the board, including Jim Messina, DNC Chair Debbie Wasserman Schultz, DSCC Chairman Bennet and DCCC Chairman Steve Israel – not to mention Senator Schumer and Senator Reid," said a spokesman for the National Republican Senatorial Committee, Brad Dayspring.

The group doesn't seem to be backing down, re-tweeting another user's defense of their tweets about Chao even after their Twitter feed became news.

@astra543 @progressky She is married to Mitch McConell is't she? It stands to reason why she wld be down on american workers, her husband

— leona barrow (@jenekool) February 26, 2013

Progress Kentucky was launched in December by a former member of the state Democratic party's executive committee. Politico's Manu Raju reported last month that it was working with tea party groups in Kentucky to try and land a primary challenger for McConnell.