(CNN) - Ramping up background checks on gun sales, which is regarded as the gun control measure with the best possible chance of gaining congressional approval, is by no means a sure thing, a key player in gun legislation negotiations said Sunday.
Sen. Tom Coburn, who is among a bipartisan group of four senators working behind the scenes on a bill to expand background checks, said a sticking point had emerged on whether to keep records on gun owners.
"I don't think we're that close to a deal," the Oklahoma Republican said on "Fox News Sunday." "There absolutely will not be record-keeping on legitimate, law-abiding gun owners in this country. If they want to eliminate the benefits of actually trying to prevent the sales to people who are mentally ill and to criminals, all they have to do is to create a record-keeping. That will kill this bill."
Coburn, who maintains an A rating with the National Rifle Association, is joined in his group by Sen. Mark Kirk, R-Illinois; Sen. Joe Manchin, D-West Virginia, a longtime advocate of gun rights; and Chuck Schumer, D-New York, a longtime supporter of gun control.
The chairman of the Senate Judiciary Committee, Sen. Patrick Leahy of Vermont, was adamant Sunday that expanded background checks would not include provisions to register gun owners, but he said that responsible Americans looking to purchase firearms shouldn't fear robust checks.
"They check to see if you told the truth, and then it's cleared out," Leahy said of the current background check system, adding later that measures to register gun owners would not be part of Senate gun control legislation.
"It's not going to be registration," he said on CNN's "State of the Union," adding that Republicans and gun advocates need to "lower the rhetoric and talk reality."
"I'm a gun owner. A lot of people in my state of Vermont are gun owners. But I know last time I went in to purchase a firearm, I had to go through a background check. I didn't have any problem with doing that," Leahy said.
At the beginning of February, sources in both parties told CNN the bipartisan group was making significant progress toward expanding background checks on gun sales, including requiring checks on private sales and closing the so-called gun show loophole.
However, the sources emphasized they were trying to work through the sticky issue in a fashion that made Republicans, particularly Coburn, comfortable that privacy concerns of gun owners were maintained. They also said any bill would include clear exemptions for situations where a background check should not be needed, such as inheriting guns from family members.
These talks are proceeding as Leahy holds hearings in the Senate Judiciary Committee and is working to find common ground on gun legislation that he can bring for a vote in his committee within the next month.
CNN Chief Congressional Correspondent Dana Bash contributed to this report.