Gun control efforts hit Senate snag Disagreement over details of how universal background checks track firearm purchases in the United States has halted momentum on further legislation, dimming -- for now -- prospects that Congress will pass major new gun laws in the wake of the Newtown shootings. Senate Democrats negotiating a bill to require all gun buyers to get a background check have abandoned discussions with GOP Sen. Tom Coburn, leaving the legislation -- at least for now -- without backing from a pro-gun Republican. That means a key Senate committee will start discussing and voting on gun laws Thursday morning without a workable, bipartisan version of what's become the centerpiece of President Barack Obama's proposed package of new gun laws. And it will make it harder to convince a wide swath of GOP senators that it's politically safe to back any major new requirements or restrictions on gun sales. The blow for gun control advocates comes on a day that former Rep. Gabrielle Giffords appeared at the Safeway supermarket in Tucson, Ariz., where she was shot in the head in 2011 as she met with constituents. Thank you very much," were all the words Giffords could muster as she stood at a podium with husband Mark Kelly. Her new political action committee, Americans for Responsible Solutions, is running ads in Arizona and Iowa pushing senators to vote for expanded background checks. Sen. Lindsey Graham holds a press briefing on Wednesday to stress the importance of keeping guns out of the hands of mentally disturbed individuals. Coburn, who carries an "A" rating from the National Rifle Association, has been negotiating with Democratic Sens. Charles Schumer and Joe Manchin on a bill that would require all gun buyers to get a background check. Under current law, Americans only have to get a background check if they're buying a gun from a licensed dealer. A Schumer aide on Wednesday said that lines of communication with Coburn are still open -- but that the senators can't agree on whether private gun sellers should be required to keep records of gun sales. As a result, Schumer has started aggressively looking for other pro-gun Republicans to sponsor the legislation. Republican Sen. Mark Kirk of Illinois has already signed on; as negotiations with Coburn have continued, Schumer has shared potential compromise language with Sens. John McCain, Jeff Flake and Susan Collins. Having an NRA A-rated senator on board would lend political cover to other Republicans to vote in favor of expanding background checks; that's why Coburn was such a promising partner in negotiations. Without him, it's unclear if another Republican would step forward -- and even Senate Democrats are wary of pushing hard on gun legislation if it wouldn't get overwhelming support. The developments also will leave the Senate Judiciary Committee -- meeting Thursday morning to consider four gun bills -- to "mark up" and vote on an old version of the background check bill. Schumer introduced the bill in the last Congress, and the full Senate will likely never vote on the language it will include. Senate Democratic aides say they expect the Senate to consider gun legislation on the floor during the first week in April. At Thursday's markup, much of the Republican ire is likely to be directed at the assault weapons ban, sponsored by Sen. Dianne Feinstein. Democratic aides expect that a gun trafficking bill with bipartisan support will pass through the committee relatively quickly. Senators will also consider a school safety measure. This story was originally published on Wed Mar 6, 2013 6:21 PM EST