Watched by tearful relatives of Newtown school-massacre victims, gun control supporters in the Senate won the first showdown over how to respond to the December shootings in Connecticut, defeating an effort by conservatives to derail firearms restrictions before debate could even start.

Thursday’s 68-31 roll call gave an early burst of momentum to efforts by President Barack Obama and lawmakers to push fresh gun curbs through Congress. The National Rifle Association, along with many Republicans and some moderate Democrats, say the proposals go too far, and the road to congressional approval of major restrictions remains rocky.

“The hard work starts now,” Senate Majority Leader Harry Reid, D-Nev., said after the vote. As he spoke, relatives of Newtown victims watching from the visitors’ gallery above the Senate floor wiped away tears and held hands, and some seemed to pray.

The vote came four months after a gunman killed 20 first-graders and six staff members at Sandy Hook Elementary School in Newtown, spurring Obama and legislators to attempt to address firearms violence. Congress hasn’t approved sweeping gun restrictions since enacting an assault-weapons ban 19 years ago, a prohibition that lawmakers did not renew a decade later.

On Thursday, 50 Democrats, 16 Republicans and 2 independents opposed the conservative effort, while 29 Republicans and 2 Democrats supported it. Gun control supporters needed 60 votes to block the conservatives.

The vote opened the door to an emotion-laden debate on the legislation, which would subject more firearms buyers to federal background checks, strengthen laws against illicit gun trafficking and increase school safety aid. Advocates say the measures would make it harder for criminals and the mentally ill to get weapons.

Opponents argue that the restrictions would violate the Constitution’s right to bear arms and would be ignored by criminals. Despite their defeat, conservatives were threatening to invoke a procedural rule forcing the Senate to wait 30 hours before it could begin considering amendments.

Before the vote, Senate Minority Leader Mitch McConnell, R-Ky., who was supporting the conservative effort, said the legislation would restrict the constitutionally protected rights of relatives and friends to sell firearms to each other.

“This bill is a clear overreach that will predominantly punish and harass our neighbors, friends, and family,” McConnell said.

After the vote, Obama spoke by phone with some Newtown families, saying he would “keep fighting for the votes they deserve.”

Expanded background checks are at the core of the gun-control drive. Other top proposals, including bans on assault weapons and high-capacity ammunition magazines, will be offered as amendments during Senate debate.