The Senate voted 68-31 to clear the way for a full debate on the package, which would expand background checks on purchasers of firearms, but the Washington publication Politico reported Senate rules mean the Republicans could throw up another minor delay by insisting a formal vote be taken Friday on opening the debate.
"Americans across this great country are looking to us for solutions and for action," said Sen. Patrick Leahy, D-Vt., chairman of the Senate Judiciary Committee.
Before the vote, family members of victims of the mass shooting at Sandy Hook Elementary School in Connecticut sought Thursday to shame senators who said they would filibuster gun control legislation, The New York Times reported.
"No one should have to experience the pain we have endured -- common-sense gun laws will help spare others from the grief we live with every day, " they said in a statement signed by 33 family members of 20 children and six educators killed by a lone gunman in Newtown, Conn., on Dec 14.
The statement, circulated by New York Mayor Michael Bloomberg's anti-gun violence group, said, "The senators who have vowed to filibuster this bill should be ashamed of their attempt to silence efforts to prevent the next American tragedy."
Politico said Senate Majority Leader Harry Reid, D-Nev., wanted to forgo the vote to move the process along but leaders of the Republican opposition did not appear willing to ease their opposition.
"Proponents say that the people deserve a vote, but don't they deserve to know what they're voting on?" said Sen. Mike Lee, R-Utah, a leader of the filibuster proponents.
Lee implied the Democrats had a hidden agenda for further restrictions on guns they were not broadcasting, Politico said, adding the GOP was expected to launch a second assault on the legislation once it reached the Senate floor in the form of a blizzard of amendments that will bog down the debate for at least a few weeks.
Notable deaths of 2014 [PHOTOS]