Washington CNN  — 

An impromptu effort to pass a gun background check bill in the Senate unanimously was quickly nixed by a Republican senator who said it would infringe on Second Amendment rights, as news of a mass shooting at a California high school came rolling in Thursday morning.

Democratic Sen. Chris Murphy of Connecticut requested that the universal background check bill, H.R. 8, be passed by unanimous consent – a procedural move that allows a bill to skip several steps, including debate, to pass unanimously, without senators casting an individual vote.

“We can’t go 24 hours without news of another mass shooting somewhere in America. My kids and millions’ others hide in corners of their classroom or in their bathrooms preparing for a mass shooting at their school, and this body does nothing about it,” Murphy, who represented the constituents of Newtown in the House of Representatives at the time of the 2012 Sandy Hook elementary school mass shooting, said on the Senate floor just before noon on Thursday.

The motion was blocked by Republican Sen. Cindy Hyde-Smith of Mississippi, who argued that the bill should not be “exempt from consideration by the appropriate committee of jurisdiction.”

“Legislation that would affect the rights of American citizens under the Second Amendment should not be fast tracked by the Senate,” Hyde-Smith said Thursday.

“If this so-called common sense bipartisan legislation was indeed crafted with strong bipartisan input, it shouldn’t have any problems advancing by regular order,” she added. “Many questions about this legislation need to be answered before it’s forced upon law-abiding gun owners.”

After Hyde-Smith’s action, Murphy said, “I can’t get a piece of legislation to the floor in any other way other than to offer this motion,” Murphy said, citing the Republican control of the committee. “And the American public are not going to accept silence from this body week after week, month after month, in the face of this epidemic carnage that is happening across this country.”

Passed in the US House of Representatives in February, H.R. 8 would require background checks on all firearm sales in the country. Currently, under federal law, only licensed gun dealers must perform background checks for anyone seeking to purchase a firearm, which leaves the sale of guns between individuals largely unregulated.

A gunman opened fire at Saugus High School in Santa Clarita Thursday morning, leaving two dead and several others injured, officials said. The suspect is in custody and is being treated at a hospital, according to the Los Angeles County sheriff.

“We have to fix this. There are bills that are currently being blocked in (Senate Majority Leader Mitch) McConnell’s Senate that would do something about this epidemic,” Democratic Sen. Brian Schatz of Hawaii tweeted early Thursday afternoon. “Kids should be safe in school. It’s the least we can do.”

CNN’s Caroline Kelly and Clare Foran contributed to this report.