Obama has called members of Congress and invited families of school shooting victims to lobby Capitol Hill, and first lady Michelle Obama has contributed to the effort with a major speech, The Hill said Saturday.
Jamal Simmons, a Democratic strategist, said the administration "has learned to use all of its assets to move things they way they hadn't done in the first term."
"They're on top of their strategic game on this issue," he said.
A senior White House official said the administration -- through dinners and meetings with lawmakers and working to "crystallize" public opinion -- has "made it known that 90 percent of the public favored background checks and that pierced through all the other noise."
Obama is "definitely gaining ground" on the issue, said Republican strategist Ken Lundberg, but the president's not assured of legislative victory because "he's not shaping the outcome."
Public opinion about gun control has seesawed between support and opposition since 20 children and six staffers were shot to death Dec. 14 in a massacre at Sandy Hook Elementary School in Newtown, Conn.
Support for some form of gun control may have strengthened with the announcement this week of a compromise proposal for a firearms sale background check bill, by Republican and Democratic senators who have top ratings from the National Rifle Association.