(CNN) -

Sen. Joe Manchin, D-West Virginia, sounded optimistic Wednesday about getting legislation that would expand background checks passed.

"I think we've got a good working group that's been moving very, very favorably forward," he said Wednesday on CNN's The Situation Room.

The senator emphasized that "nobody is going to take anybody's guns away."

"What we're saying is that if you buy a gun, transfer a gun, there should be a criminal and a mental background check," he said.

That would include transactions at gun shows, online sales and individual transfers. Those handing down guns to family members, however, would be exempted.

Gabrielle Giffords, a former congresswoman shot and wounded more than two years ago, urged support for background checks on Wednesday.

She and her husband, Mark Kelly, spoke at a gun control rally in Tucson, Arizona, the same place where an assailant shot her in the head. They have been leading voices in the fight for tougher background checks.

Kelly said his newly formed gun-control organization, Americans for Responsible Solutions, is sending a letter to U.S. Sens. John McCain and Jeff Flake, both Arizona Republicans, urging them to support background-check legislation. McCain suggested last month that such legislation would have success in the Senate.

Manchin said he has been working with Republican Sens. Mark Kirk of Illinois and Tom Coburn of Oklahoma. Asked by CNN's Wolf Blitzer if Coburn was fully on board, Manchin said he couldn't speak for his fellow senator but added he's "very hopeful" that Coburn will back the bill.

Responding to comments by National Rifle Association executive director Wayne LaPierre - who claimed lawmakers were trying to register peoples' guns - Manchin said LaPierre must have been referring to other legislation.

"We've been working with NRA, and hopefully, they've understood where we're coming from," he said. "What we're doing bans any registry."

While Manchin mentioned there may be other pieces of legislation in the works by different lawmakers, he maintained that the one he's working on appears to be the only bill that has the possibility of bipartisan agreement.

Other proposals to combat gun violence include limiting magazine capacities. But Manchin said that's not in their legislation and they're "not ready to deal with it."

"Our legislation has a commission on mass violence," he said. "Everyone's looking at the guns, and sure, that's the end result of what happens. The bottom line is, how does someone get a gun? How does someone use or not use a gun properly?"

Manchin said it's unlikely that an assault weapons ban would become law.

"That's not going to pass," he said "I do not support that."