The decision comes one day after Senators rejected several proposals for new gun controls.
Gun rights advocates are calling the votes a victory.
"This incremental approach to restricting people's rights was put to a stop yesterday, and so we were pleased to see that," said Erich Pratt of Gun Owners of America.
Tucson shooting survivor Gabby Giffords took to the New York Times.
She writes "speaking is physically difficult for me. But my feelings are clear: I'm furious".
She and her husband Mark Kelly fought hard for the expanded background checks that were rejected.
An assault weapons ban and limits to ammunition clips also failed.
Her husband, former astronaut Mark Kelly, called the votes a "terrible day for America".
"If the Senate will not do their jobs and work to keep our community safer, then we're going to have to change who's actually in Congress," Kelly said.
Republican Senator John Cornyn denied accusations he rejected the proposals out of fear of the gun lobby.
"I don't listen to them. I work for 26 million Texans," Cornyn said.
Senate Majority Leader Harry Reid argued Cornyn and his colleagues who opposed the bill ignored the will of most Americans.
"Republicans are in an unsustainable position, crosseyes with nine out of ten Americans," Reid said.
Supporters of gun control are asking those Americans to pressure their Senators and save any hope for new federal gun laws.
Democrats say they will bring the original gun bill up for a vote eventually, but for now, it's on hold.
They're buying time to rally enough support to save it from failing as well.
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