(NewsNation) — The Senate easily approved a bipartisan gun violence bill Thursday that seemed unthinkable a month ago, setting up final approval of what will be Congress’ most far-reaching response in decades to the nation’s run of brutal mass shootings.

The bill passed 65-33 in the evenly-divided Senate. It will now move to the House.

“This is not a cure-all for the all the ways gun violence affects our nation,” said Senate Majority Leader Chuck Schumer, D-N.Y., whose party has made gun restrictions a goal for decades. “But it is a long overdue step in the right direction. Passing this gun safety bill is truly significant, and it’s going to save lives.”

Senate Minority Leader Mitch McConnell, R-Ky., said “the American people want their constitutional rights protected and their kids to be safe in school.” He said “they want both of those things at once, and that is just what the bill before the Senate will have accomplished.”

The legislation would toughen background checks for the youngest firearms buyers, require more sellers to conduct background checks and beef up penalties on gun traffickers. It also would disburse money to states and communities to improve school safety and mental health initiatives.

The legislation would also prevent people convicted of domestic abuse, but are not married to their partners, from owning a firearm.

Aides told The Associated Press the move would cost $13 billion.

The election-year package fell far short of more robust gun restrictions Democrats have sought for years, including bans on the assault-type weapons and high-capacity ammunition magazines used in the slayings in Buffalo, New York, and Uvalde, Texas.

Yet the accord let leaders of both parties declare victory and demonstrate to voters that they know how to compromise and make government work, while also leaving room for each side to appeal to its core supporters.

Tellingly, GOP senators voting “no” included potential 2024 presidential contenders like Tom Cotton of Arkansas, Ted Cruz of Texas, Josh Hawley of Missouri and Tim Scott of South Carolina.

Some of the party’s most conservative members voted “no” as well, including Sens. Rand Paul of Kentucky and Mike Lee of Utah.

Less than one-third of the Senate’s 50 GOP senators backed the measure and solid Republican opposition is certain in the House.

Top House Republicans urged a “no” vote in an email from the No. 2 GOP leader, Rep. Steve Scalise of Louisiana, that called the bill “an effort to slowly chip away at law-abiding citizens’ 2nd Amendment rights.”

The Associated Press contributed to this report.