Senate Democrats said Tuesday that they're eager to turn back to the issue of gun control — but admitted it won’t happen any time soon.

Sens. Patrick Toomey (R-Pa.) and Joe Manchin III (D-W. Va.), in a recent joint appearance on CBS’ “Face the Nation.” (AP)

"I don’t know exactly when it’s going to come back exactly on the Senate floor, but I’m very happy that we have some Republicans who are talking out loud that they’d like to take another look at this," Senate Majority Leader Harry M. Reid (D-Nev.) told reporters Tuesday.

Reid said he met with voters during last week's congressional recess who "shook their heads in dismay that the Republicans here in Congress – and not all Republicans feel this way – Republicans here in Congress feel that if someone has deep, severe mental problems they should be able to buy a gun. Or that someone who’s a criminal should be able to buy a gun. I’m in lockstep with the American people, and I don’t know about the NRA, but I’d rather be in lockstep with the American people."

Reid's comments came as top Senate aides said that at least two unnamed Republican senators had approached Democrats in recent days about engaging once again in discussions about new gun laws.

But two GOP senators who voted against a bipartisan background check plan said Tuesday that any new agreement would have to be radically different than the one rejected by the Senate last month.

“I’m not reconsidering my position, I think they ought to go back to the drawing board," Sen. Jeff Flake (R-Ariz.) said. "I want to strengthen our background check system, but whether they can do that with the Toomey-Manchin proposal, I don’t know."

Sens. Joe Manchin III (D-W. Va.) and Patrick J. Toomey (R-Pa.) authored the plan that would have expanded the national gun background check system to include most commercial firearms sales, including transactions completed on the Internet.

Flake said Tuesday that he's in "no active discussions" with Toomey and Manchin, adding that "They’ve got to go back to the drawing board."

For Flake, "The biggest thing is commercial sales is defined too broadly," he said. "Virtually anything that touches the Internet – text messages, any posting – is a commercial sale. That’s far, far too broad.”

Sen. Johnny Isakson (R-Ga.), who also voted no on the bipartisan plan, said Tuesday that “I’m not going to change my vote.”

Isakson met Monday in his Atlanta office with a group of gun-control advocates and told them that he has spoken with Manchin and Toomey about their plan. But he said Tuesday that he doesn't think he could support any new proposal to stiffen gun laws, adding that "just because I meet with someone doesn’t mean I’m going to change my view.”

And Sen. Kelly Ayotte (R-N.H.), who is facing a barrage of television ads back home for voting against the proposal, reiterated Tuesday that she voted for a GOP plan that would have fixed the national background check system by requiring states to provide the Justice Department with more information on people who are mentally ill and incapable of owning firearms.

One Democrat who voted against the plan, Sen. Mark Pryor (Ark.), said he's also open to exploring the issue again. "If they want to make changes or draft new legislation, I'll certainly look at it. But I don't have a definitive list of things in mind that I need to see," he told reporters.

On Tuesday, Manchin used a phrase he's used often when asked about the gun issue: "We’re still working. We're still talking."

"People are very concerned and very interested, we’ll just keep talking and trying to find that area where we can maybe be clear in our definitions and intent in some areas," he added.

Key to restarting debate on the issue of gun control would be a new groundswell of support for stricter gun laws among the general public, according to legislative aides and activists. Supportive lawmakers are waiting to see whether a new public campaign by gun-control groups and the White House will put enough pressure on senators who voted no to reconsider.

Follow Ed O'Keefe on Twitter: @edatpost