Obama, Biden re-up gun talks with GOP senators Updated: 11:31 a.m. As the Senate prepares to vote on perhaps the most critical piece of the Obama administration's gun safety proposals, President Obama and Vice President Joe Biden have met privately with a handful of Republican senators in a behind-the-scenes push to gin up success, according to the Hill. According to a White House official, Mr. Obama and Biden both met with Sens. John McCain, R-Ariz., and Lindsey Graham, R-S.C., and Biden met privately with Sen. Johnny Isakson, R-Ga., as well. The Hill reports that the VP is calling his former colleagues in the Senate on a "near-daily" basis and that he will be spending "considerable" time on Capitol Hill in the coming weeks. Biden has been a key actor in the administration's efforts to pass a package of new gun measures since early this year, and Mr. Obama has recently taken up a more personal approach to retail politics, showing up on Capitol Hill for meetings and hosting meals with his Republican adversaries. With a Senate vote on the horizon for a bill that would strengthen background checks for gun purchases, their efforts could be critical in finding the 60 votes necessary to overcome a filibuster and pass the legislation. Sen. Chuck Schumer, D-N.Y., said yesterday he is "working very hard with both Democrats and Republicans, pro-NRA and anti-NRA people" to develop a background check bill that will be "acceptable to 60 senators and be very strong and get the job done." "It's very hard," he said in an interview on NBC's "Meet the Press." We're working hard and I'm very hopeful that we can get this passed. Despite the formidable opposition to new gun measures - including in the GOP-controlled House of Representatives - some Republicans are showing a willingness to discuss the options on the table. Yesterday, Graham told CNN he would not block the bill unless Sen. Majority Leader Harry Reid, D-Nev., didn't allow alternative amendments. "I'd like to have an open process," he said. I have legislation with Senator Pryor and Begich, two Democrats, myself, and Jeff Flake, that would change the federal system... There's all kind of bipartisan legislation out there that I think would keep guns out of the hands of people who are mentally ill, shouldn't have a gun, and there's some real efforts out there to beef up prosecutions of those who fail a background check.