By Ashley Killough, Jim Sciutto and Miranda Green, CNN

(CNN) -- Former Democratic presidential nominee Hillary Clinton, amid the fallout of the massacre in Las Vegas, turned the political spotlight on a gun bill that's currently making its way through the House.

"The crowd fled at the sound of gunshots. Imagine the deaths if the shooter had a silencer, which the NRA wants to make easier to get," she tweeted Monday morning.

She wrote later, "Our grief isn't enough. We can and must put politics aside, stand up to the NRA, and work together to try to stop this from happening again."

The "Hearing Protection Act," which would make it easier to purchase silencers, is part of a larger bipartisan measure that would ease restrictions on transporting guns across state lines and narrows the restricted category of armor-piercing ammunition. Supporters point out that silencers don't make guns silent, but it decreases their decibel level and muffles the noise.

The House Committee on Natural Resources passed the bill last month. It aims to "expand opportunities for hunting, fishing, and recreational shooting" and "increases safety and hearing protection for sportsmen and women," according to a statement from the committee at the time of passage. The bill would now go to a floor vote, and would need to pass the Senate, but no such vote has been scheduled in the House.

When authorities stormed the room of the Las Vegas gunman on the 32nd floor of the Mandalay Bay hotel, authorities found a cache of weapons, including 10 rifles, Las Vegas Metropolitan Police Sheriff Joseph Lombardo told reporters over night. Authorities have not said whether any silencers had been found or were used among the shooters' weapons cache.

A congressional hearing on the legislation had been scheduled for the bill in June, but was canceled in the wake of the shooting at a Republican congressional baseball practice that seriously wounded House Republican Whip Steve Scalise and several others.

Arizona Democratic Rep. Ruben Gallego, who is on natural resources committee, told CNN on Monday that the only thing between the bill and its passage is "timing."

"The current system for background checks for silencers is very important," Gallego said. "The only thing that's stopping Republicans now is timing."

Multiple GOP leadership aides say there is no House floor vote scheduled yet on that measure.

Clinton repeatedly brought up the need for tougher gun control laws during the 2016 president campaign. The previous deadliest mass shooting in modern US history -- the shooting at Orlando's Pulse nightclub which killed 49 people -- occurred in June 2016, during last year's presidential election. With authorities saying 58 people were killed in Vegas, the most recent shooting now becomes the country's deadliest mass shooting in modern history.

This story has been updated and will continue to update with additional information.