In an Associated Press-GfK Poll last month, requiring more background checks got overwhelming public support, compared to just over half who backed bans on assault weapons and high-capacity ammunition magazines.
"The whole goal is to keep guns out of the hands of the mentally ill and criminals," Coburn said in a brief interview.
Manchin's support could make it easier to win backing from other Democratic senators from GOP-leaning states, many of whom face re-election next year and who have been leery of embracing Obama's proposals.
"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."
Schumer and Kirk each have "F'' scores from the NRA for their voting records in Congress, while Coburn and Manchin have "A'' ratings.
Though widened background checks is given the strongest chance for enactment of Obama's major proposals, 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.
"That's the way reductions in liberty occur, when you start saying people have to sign up for something and they have a database where they know exactly who's who," Sen. Orrin Hatch, R-Utah, said in an interview.
Gun control supporters note that federal laws specifically forbid the national background check system from being used as a registry of gun owners. Much of the information the system collects must be destroyed within a day.
NRA spokesman Andrew Arulanandam declined to comment on the senators' discussions.
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.
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.