A deal, given a good chance by several participants and lobbyists, could add formidable political momentum to one of the key elements of President Barack Obama's gun control plan. Currently, background checks are required only for sales by the nation's 55,000 federally licensed gun dealers, but not for gun show, person-to-person sales or other private transactions.

The senators' talks have included discussions about ways to encourage states to make more mental health records available to the national system and the types of transactions that might be exempted from background checks, such as sales among relatives or to those who have permits to carry concealed weapons, said people who spoke anonymously because they were not authorized to describe the negotiations publicly.

The private discussions involve liberal Sen. Chuck Schumer of New York, who is the No. 3 Senate Democratic leader; West Virginia Sen. Joe Manchin, an NRA member and one of the chamber's more moderate Democrats; Sen. Tom Coburn, R-Okla., another NRA member and one of the more conservative lawmakers in Congress; and moderate GOP Sen. Mark Kirk of Illinois.

"It will not limit your ability to borrow your Uncle Willie's hunting rifle or share a gun with your friend at a shooting range," Schumer said last week in one of the senators' few public remarks about the package the group is seeking. He said he believed a bipartisan deal could be reached.

Polls show that requiring background checks for nearly all gun purchases has more public support than Obama's proposals to ban assault weapons and high-capacity ammunition magazines, and it is among those given the best chance of enactment. Even so, it is opposed by the NRA and many congressional Republicans, who consider it intrusive and unworkable for a system they say already has flaws.

"My problem with background checks is you're never going to get criminals to go through background checks," Wayne LaPierre, NRA executive vice president, told the Senate Judiciary Committee at its gun control hearing last week.

An agreement among the four senators could help overcome that opposition by opening the door to support from other conservative Republicans besides Coburn. It also could make it easier to win backing from Democratic senators from GOP-leaning states, many of whom face re-election next year and who have been leery of embracing Obama's proposals.

Schumer and Kirk each have "F'' scores from the NRA, while Coburn and Manchin have "A'' ratings.

Prompted by the December massacre of 20 first-graders and six adults in Newtown, Conn., the Democratic-led Judiciary Committee plans to write gun control legislation in the next few weeks. The committee's chairman, Sen. Patrick Leahy, D-Vt., has expressed strong support for universal background checks and it is expected to be a cornerstone of his bill, but a version of that language with bipartisan support could give the entire package a boost.

"If the language is meaningful, it would be obviously a huge step," said Josh Horwitz, executive director of the Coalition to Stop Gun Violence, which represents child welfare, religious and other groups favoring gun curbs. "To have someone like Coburn, who's voted consistently with the gun lobby, to come out and endorse a meaningful background check would be very helpful."

It is likely that any gun-control bill will need 60 votes to pass the 100-member Senate. Democrats have 55 votes, including two Democratic-leaning independents.

Leaders of the GOP-run House are planning to see what, if anything, the Senate passes before moving on gun legislation. Strategists believe that a measure that passes the Senate with clear bipartisan support could pressure the House to act.

Federal data on gun purchases is gathered by the National Instant Criminal Background Check System, which is run by the FBI.

According to Justice Department estimates, the federal and state governments ran 108 million background checks of firearms sales between 1994 when the requirement became law and 2009. Of those, 1.9 million — almost 2 percent — were denied, usually because would-be purchasers had criminal records.

People legally judged to be "mentally defective" are among those blocked by federal law from firearms purchases. States are supposed to make mental health records available to the federal background check system and receive more generous Justice Department grants if they do, but many provide little or no such data because of privacy concerns or antiquated record-keeping systems.

Coburn got involved in the background check talks about two weeks ago and says a compromise could make it harder for dangerous people to acquire firearms.

"The whole goal is to keep guns out of the hands of the mentally ill and criminals," he said in a brief interview.

Manchin could be particularly influential with Democrats like Sens. Mark Begich, D-Alaska, and Mark Pryor, D-Ark., who face re-election next year in deeply Republican states. Besides being an NRA member, Manchin ran a campaign ad in 2010 in which he promised to defend West Virginian's Second Amendment rights to bear arms and "take on" the Obama administration — all while shooting a hole in a copy of a Democratic bill that would have clamped limits on greenhouse gases — another sore spot for a coal-mining state like West Virginia.

In an interview, Manchin said that besides hoping for a background check compromise, he wanted inclusion of a commission that would study "how our culture has gotten so desensitized toward violence."

Participating senators declined to provide details of the talks. But people following the discussions say the talks have touched on:

—The types of family relatives who would be allowed to give guns to each other without a background check.

—Possibly exempting sales in remote areas.

—Whether to help some veterans who sought treatment for traumatic stress disorder — now often barred from getting firearms — become eligible to do so.

An NRA spokesman, Andrew Arulanandam, declined to comment on the senators' discussions.