WASHINGTON – A cornerstone of President Obama’s drive to check gun violence is gathering bipartisan steam as four senators, including two of the National Rifle Association’s congressional champions, privately seek compromise on requiring far more firearms purchasers to undergo background checks.

The talks are being held even as Obama’s call to ban assault weapons and high-capacity ammunition magazines, the two other major pillars of his plan, are hitting rough waters on Capitol Hill. An agreement among the four senators to expand background checks would add significant impetus to that high-profile proposal by getting the endorsement of a group that ranges from one of the Senate’s most liberal Democrats to one of its most conservative Republicans.

“We’ll get something, I hope. I’m praying for it,” said Sen. Joe Manchin, D-W.Va., one of the participants.

Manchin, a moderate, is an NRA member who aired a 2010 campaign ad in which he literally shot a hole through Democratic environmental legislation that he pledged to oppose.

Also involved is Sen. Tom Coburn, R-Okla., another NRA member with a strong conservative record but occasional maverick impulses; No. 3 Senate Democratic leader Charles Schumer of New York, a liberal; and moderate GOP Sen. Mark Kirk of Illinois.

Background checks are required only for sales by the nation’s 55,000 federally licensed gun dealers, but not for private purchases like those at gun shows, online or in person.

There are few indisputable, up-to-date statistics on how many guns change hands without background checks, but a respected study using 1990s data estimated that 30 percent to 40 percent of gun transactions fit into that category.

The senators’ talks have included discussions about how to encourage states to make more mental health data available to the federal system for checking gun buyers’ records, according to several sources..