Ms. Ayotte said Thursday that she would continue talking with Ms. Gillibrand and was confident that some areas of agreement, on areas like expanding mental health care, could be reached.

“There’s a lot we have agreement on in terms of enforcing our current system,” she said. “And so I certainly think we should look for the common elements, including the mental health piece, which I support as well, and try to move as much of that as possible forward.”

Ms. Ayotte — the only one out of 22 senators on the East Coast north of Virginia who voted against strengthening background checks — has been the target lately of some of the most furious lobbying by gun control proponents, who have inundated local newspapers with letters to the editor denouncing her vote, run radio ads saying she “ignored the will of the people” and swamped her office with phone calls. On Thursday, two receptionists placed one call after another on hold as they politely listened to callers vent and replied, “Thank you for your message.”

Next week when Congress is in recess, gun control groups coordinating with the Obama committee Organizing for Action will be fanning out across the country in dozens of demonstrations at the offices of senators who voted down the background check bill.

As talks moved ahead on Capitol Hill, the White House was pressing on with its own efforts. Vice President Joseph R. Biden Jr. summoned a group of gun control proponents to his office on Thursday — including representatives from Michael R. Bloomberg’s Mayors Against Illegal Guns, Gabrielle Giffords’s Americans for Responsible Solutions and the Brady Campaign to End Gun Violence — and reassured them that the issue had become his highest priority.

The vice president recalled the long struggle to enact the Brady Bill, which established a five-day waiting period to buy a gun. And he told them gun control would become his new campaign to end the Iraq war, according to two participants in the meeting, comparing it to the issue he devoted much of his energy to during President Obama’s first term. The pressure campaign is evidently already starting to take its toll, the vice president added, because several senators have confided to him that they are feeling the backlash from constituents.