The most sweeping gun control legislation to come before Congress in decades cleared a key procedural hurdle in the Senate on Thursday, launching what will be weeks of floor debate over whether to tighten the nation's firearms laws in the wake of the Sandy Hook Elementary School shooting.

With relatives of Sandy Hook victims watching from the public gallery above, the Senate voted 68-31 to squash a planned Republican filibuster and send to the floor a bill that would create universal background checks for gun buyers.

The vote followed a week of intense lobbying by the Obama administration, which flew Sandy Hook families from Connecticut to Washington aboard Air Force One so they could go from one Senate office to the next, pressing lawmakers to back stricter gun control.

Just as the Senate was preparing to vote, the families from Newtown, Conn., issued a statement declaring that lawmakers who voted against it "should be ashamed of their attempt to silence efforts to prevent the next American tragedy."

Fourteen pro-gun Republicans intended to block the gun bill from passing, but 15 of their fellow Republicans joined with Democrats to prevent their filibuster. Republicans didn't necessarily vote for the bill because they support it but because Senate Majority Leader Harry Reid, D-Nev., promised they could add amendments of their own, some of which could ultimately lead to the bill's demise.

The progress made on the legislation is due in part to two senators from pro-gun states -- Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa. -- who this week struck a bipartisan compromise on background checks. The Manchin-Toomey deal, which will be the first amendment offered to the bill, would expand background checks to include gun shows and Internet sales but would specifically exempt firearms exchanged by family members.

"I think the issue needs to be debated," Sen. Saxby Chambliss, R-Ga., who voted to start debate, told The Washington Examiner. "Too many incidents have happened in the country, and in my opinion, it is not because of guns but because of other issues, and we need to have the debate. I don't support the underlying bill."

The National Rifle Association is now trying to derail the legislation, warning lawmakers that the nation's most powerful gun lobby could turn against them in the 2014 elections.

"I don't underestimate the difficulty in the fight ahead," Sen. Richard Blumenthal, D-Conn., one of the top advocates for the gun control measure, said after Thursday's vote. "We have faced an uphill climb every step of the way on this measure, and we are prepared for continuing odds against us."

Even if it cleared the Senate, the bill faces serious opposition in the House. Speaker John Boehner, R-Ohio, on Thursday showed little enthusiasm for expanding background checks, noting that few people have been prosecuted for violating current background check rules.

"I would think that before we begin to add more rules and regulations on law-abiding citizens," Boehner said, "that we at least expect our law enforcement personnel and the Department of Justice to enforce the current law, which they are not doing."

Gun control proponents on Thursday were buoyed by the Senate vote, the most dramatic step toward tighter gun laws since Congress banned assault weapons in 1994, a restriction that expired a decade later.

"Five days ago nobody thought we could move forward," Blumenthal said. "And we are moving forward."