Updated 6:43 p.m. |

Former Kentucky Secretary of State Trey Grayson (R) will co-lead the PAC with Robert Reich, the Democrat who served as Labor secretary under President Bill Clinton.

Grayson ran for the open Senate seat in Kentucky in 2010, losing the Republican primary to Sen. Rand Paul. Grayson had the backing of Senate Minority Leader Mitch McConnell (R-Ky.). McConnell continues to face questions from conservative activists and radio hosts about supporting Grayson over Paul, one of the political stars of the tea party movement.

Conservatives mistrusted Grayson throughout the primary process. His involvement with a PAC helmed by a Democrat could raise more questions about his political views with conservatives. Once he lost the GOP primary, Grayson accepted a position as the director of institute of politics at the Kennedy School of Government at Harvard University.

In an interview, Grayson said that while the PAC was likely to support Democrats willing to work with Republicans, he remains a proud member of the GOP. He said Giffords was a friend, which is why he was willing to lend his name to the effort.

Grayson said he has now registered to vote in Massachusetts and support Republicans in the often liberal-leaning state.

“I’ve got my Scott Brown and Mitt Romney bumper stickers on my car,” Grayson said.

He said criticism from conservatives about his latest decision to reach out to the Democratic side is not unexpected, given the partisan crowd. He added, however, that a swing through the Democratic National Convention as part of his work at Harvard only reinforced that he is a Republican.

“I’m not the player-to-be-named-later in the Artur Davis trade,” he said, in reference to the former Democratic Member from Alabama who spoke at last week’s Republican National Convention.

Reich now works as a professor of public policy at the University of California-Berkley.

Giffords resigned her House seat in January, a year after being shot in the head outside a Safeway in Tucson, Ariz., while hosting a constituent service event. She resigned to more fully concentrate on the recovery from the brain injury caused by the bullet of would-be assassin Jared Lee Loughner.

Loughner pleaded guilty last month to six counts of murder and 13 counts of attempted murder in relation to the shooting. Giffords and her husband, astronaut Mark Kelly, announced the PAC in a joint news release.

“Gabby PAC will only support candidates who are dedicated to working hard for commonsense, bi-partisan solutions that strengthen our communities and our entire country,” the release said. “This commitment to public service over partisanship is what guided Gabby while she was serving the people of Arizona and will be the guiding principle of Gabby PAC.”