(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."

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 larger package, known as the SHARE Act, 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 bill had been scheduled 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.

The House Committee on Natural Resources eventually held a hearing September 12 and passed the bill a day later. Multiple GOP leadership aides told CNN there is no House floor vote scheduled yet on the measure.

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."

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.

"The Hearing Protection Act" was introduced by Rep. Jeff Duncan, R-South Carolina, who has spoken publicly about suffering hearing loss in his left ear after growing up hunting without earmuffs or suppressors.

Currently, federal laws are more restrictive for silencers than firearms. Buyers must undergo a nine-month approval process that involves getting fingerprinted and submitting a photo, along with paying a $200 tax. The bill calls to eliminate those steps and make purchasing a silencer as easy as purchasing a firearm.

One key supporter of silencers is Donald Trump, Jr., the President's eldest son and an avid hunter. He appeared in a video for SilencerCo last year.

As seen with other recent mass shootings, some Democrats were quick to ramp up pressure Monday to enact more gun control.

"To my colleagues: your cowardice to act cannot be whitewashed by thoughts and prayers," Democratic Sen. Chris Murphy of Connecticut tweeted. "None of this ends unless we do something to stop it."

"We need to stop the carnage. More talk and prayers will not save lives. Only action and real changes in our laws can," Sen. Ben Cardin, D-Maryland, tweeted.

Others were more specific about weaponry.

"When you have weapons of war in wide circulation, you get war-like casualty counts. Not what the Founders had in mind," Sen. Jeff Merkley, D-Oregon, tweeted. "House bill for easier access to silencers = more carnage in these kinds of shootings. Terrible idea."

"Congress should take up and vote on legislation to ban military-style weapons," Sen. Bob Casey, D-Pennsylvania, tweeted.