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.

Read More