Democrats Quietly Renew Push for Gun Measures WASHINGTON - Democratic leaders in Congress and the White House renewed their push for gun legislation on Thursday, just months after it was defeated in the Senate, amid delicate talks on a new background-check measure that advocates hope could change enough votes from no to yes. But those negotiations met a warning from Senator Harry Reid of Nevada, the majority leader, who said he would not accept any bill that is substantially weaker than the one defeated in April. "The bill that passes the Senate must have background checks, and not a watered-down version of background checks," Mr. Reid declared in the Capitol, flanked by the families of Newtown, Conn., school shooting victims. Those families also visited President Obama on Thursday at the White House and Speaker John A. Boehner. Quiet talks between Senators Mark Begich, Democrat of Alaska, and Kelly Ayotte, Republican of New Hampshire, officially do not exist. Both senators voted no in April, and aides to both deny the existence of negotiations or legislation. "There are no talks," said Jeff Grappone, a spokesman for Ms. Ayotte. There is no legislation. She stands by her vote. But other senators are openly acknowledging and encouraging the effort and say the talks are building momentum. Senator Richard Blumenthal, Democrat of Connecticut, said a new version of the gun bill would most likely enhance prosecutions of those who violate existing gun laws and further clarify that new legislation would not and could not lead to a national database of guns or gun ownership. Other Democrats said the defeated background check measure, written by Senators Joe Manchin III, Democrat of West Virginia, and Patrick J. Toomey, Republican of Pennsylvania, would probably be amended to exempt more rural sales and person-to-person sales from mandatory checks. "We have to give them a credible and commendable way to change their votes," Mr. Blumenthal said of a handful of senators who could be persuaded, starting with Mr. Begich and Ms. Ayotte. Such modifications do not have to weaken the bill substantially, he added."Sometimes clarification can have the appearance of change," he said. Six months after the massacre at Sandy Hook Elementary School in Newtown, the emotions of the gun issue are still raw. Jillian Soto, whose older sister was one of the teachers killed in Newtown, told lawmakers, "America has not forgotten." Americans remain broadly supportive of legislation that expands background checks on gun purchases but are skeptical that such a bill will pass. A New York Times/CBS News poll released this month found that 69 percent support passage of a measure to expand such checks, but 56 percent say that significant change to gun policy is not likely this year. But while Democratic leaders insisted Thursday that passage of a tough gun bill was inevitable, the numbers are daunting. Advocates of expanded gun background checks need five senators to change their votes, and a sixth vote if New Jersey's newly appointed Republican senator, Jeffrey S. Chiesa, is opposed. Senators pressing forward believe that if Ms. Ayotte and Mr. Begich could strike an accord, they could bring along Senator Heidi Heitkamp, Democrat of North Dakota, and possibly Senators Max Baucus, Democrat of Montana, Lisa Murkowski, Republican of Alaska, and Jeff Flake, Republican of Arizona. But on Thursday Ms. Heitkamp, Mr. Flake and Mr. Baucus either avoided the question about changing their votes or said they had no intention of doing so. "I've had a lot of these conversations," Mr. Toomey said. I'm not aware of any real movement on the part of people who opposed it last time. Democrats are also divided over how to pressure members of their own caucus to get behind a new push. Senator Christopher S. Murphy, Democrat of Connecticut, praised what he called "the political infrastructure" emerging to push gun control, and said "members who voted no are not real excited about having to face hundreds of thousands of dollars of ads" from groups like Mayors Against Illegal Guns, which was founded by Mayor Michael R. Bloomberg of New York. But Democratic leaders are increasingly vocal in their admonitions against Mr. Bloomberg's attacks on Democrats who voted no in April. Mr. Reid said Thursday that he spoke to the mayor this week to impress on him that "to have Republicans control the Senate is a sure sign we will never, ever get anything done." Mr. Reid was not sure that message had gotten through. "He's kind of a free spirit, and a very rich one," he said.