Toomey, who crafted a deal with Sen. Joe Manchin, D-W.Va., said in an appearance with Manchin on CBS' "Face the Nation" at least three of GOP his colleagues will support the amendment, but noted it still has a long way to go to become law.
"We're close," Toomey said. "We're discussing with colleagues on both sides. We've got bipartisan support, but there is bipartisan opposition."
He said others had told him unofficially they would support the measure, but conceded its ultimate fate remains unknown.
"It's very hard to say what amendments may succeed and which may fail," Toomey conceded.
But, he added, "ours, I think, just strikes the right balance."
Manchin, a gun rights advocate, said the measure was not a universal background check, which gun control advocates favor. The expanded checks would be solely to screen out the mentally ill and criminals.
"This is not universal, let me be very clear," Manchin said. "This is a criminal and mental background check bill; only at gun shows and Internet sales. There's going to be some people who said you didn't go far enough. Some are saying you went too far. But if they'll look at the bill, what we did, we did right. And we have cut down, the gun, the loophole in the gun shows and those on Internet sales, and that's what we tried to do. And we made no, no exceptions on that."