President Barack Obama praised the bipartisan compromise U.S. Sens. Joe Manchin, D-West Virginia, and Pat Toomey, R-Pennsylvania, struck Wednesday that would strengthen background checks on gun purchases.

“This is not my bill, and there are aspects of the agreement that I might prefer to be stronger,” Obama said in a statement. “But the agreement does represent welcome and significant bipartisan progress. It recognizes that there are good people on both sides of this issue, and we don’t have to agree on everything to know that we’ve got to do something to stem the tide of gun violence.”

The bipartisan bill would require background checks on gun sales in commercial settings, including at gun shows and on the Internet. It also ensures that more people who are federally prohibited from having guns are included in the background check system by improving state reporting systems. And it allows licensed firearm dealers to do background checks on their employees.

But the bill still needs to reach the Senate floor.

“The Senate must overcome obstruction by defeating a threatened filibuster, and allow a vote on this and other common sense reforms to protect our kids and our communities,” Obama said.

That’s only the first obstacle. Even if it passed the Senate, the bill would still need to clear the Republican-led House.

U.S. Sen. Richard Blumenthal remained optimistic the bill will be called for a vote.

“The majority of Americans want a vote, and they want action from this body,” Blumenthal said. “And we need to keep faith with them but also with the victims — the victims who should not be forgotten. The Connecticut effect is not going away. This resolve is not dissipating. We will keep faith with them.”

The U.S. Senate will need 60 votes to proceed with the bill. There are 53 Democrats in the U.S. Senate and two independents who traditionally vote with them. That means there will need to be Republican support for the measure.

The National Rifle Association remained opposed to bipartisan compromise.

“Expanding background checks at gun shows will not prevent the next shooting, will not solve violent crime and will not keep our kids safe in schools,” the NRA said in a statement.

“The sad truth is that no background check would have prevented the tragedies in Newtown, Aurora or Tucson,” it said. “We need a serious and meaningful solution that addresses crime in cities like Chicago, addresses mental health deficiencies, while at the same time protecting the rights of those of us who are not a danger to anyone.”