Two GOP and two Democratic senators have been looking for a compromise on requiring more of the checks, currently required only for transactions by federally licensed dealers. Private transactions at gun shows, online and elsewhere are not covered by the system, which is designed to keep firearms from criminals, people with serious mental problems and others.
The senators have been bargaining quietly over ways to expand the checks to private sales. But Sen. Tom Coburn, R-Okla., a conservative who has taken a leading role in the talks, has opposed requiring record keeping for private transactions because of a concern it could lead to a national registry of gun owners, which is vehemently opposed by the National Rifle Association and other gun rights groups.
Democrats say keeping records of private sales is the only way to ensure the checks are performed, and say fears of the creation of a federal gun registry are unfounded. They have offered to have gun manufacturers or other private entities, not the government, keep those records.
The talks were described by a Senate aide and a lobbyist who spoke on condition of anonymity because the senators' talks are private and considered extremely politically sensitive.
The other senators participating in the bargaining are liberal Charles Schumer, D-N.Y., moderate Joe Manchin, D-W.Va., and moderate Mark Kirk, R-Ill.
An agreement involving the influential Coburn could be pivotal because it could pave the way for other Republicans to support a background check bill.
Coburn said Sunday that he opposed keeping records on "legitimate, law-abiding gun owners."
"All they have to do is create a record keeping and that will kill this bill," he said on "Fox News Sunday."
The bargainers are close to agreement on other parts of the background check compromise, including carving out exemptions for sales between close relatives and for people who have already been cleared to receive concealed carry permits. They are also working toward creating an appeals process for veterans initially denied guns because they have been treated for traumatic stress disorder.
Chairman Patrick Leahy, D-Vt., of the Senate Judiciary Committee is hoping his panel can begin writing gun control legislation this week, but that is considered likely to slip until the following week. His panel is expected to approve legislation on background checks and stiffer federal penalties against illegal gun trafficking.
It is unclear whether there will be enough votes to approve two other Obama priorities: bans on assault weapons and magazines carrying more than 10 rounds of ammunition.