Sen. Kelly Ayotte, R-New Hampshire, voted with fellow Republicans for Cornyn and Grassley's measures, but against Murphy's. She broke with party lines to vote for Feinstein's amendment.
Another embattled Republican, Sen. Mark Kirk, R-Illinois, voted in favor of the two Democratic-backed amendments. Kirk, who co-sponsored Feinstein's amendment, was the only Republican senator to vote in support of barring those on the terror watch list from buying guns in December 2015.
With Sen. Bernie Sanders, I-Vermont, returning for his second vote of the year, all 100 senators voted for the first time this year.
Dan Gross, president of the Brady Campaign to Prevent Gun Violence, said in a statement following the vote, "Shame on every single senator who voted against these life-saving amendments and protected the rights of terrorists and other dangerous people to buy guns."
Feinstein's so-called "no fly, no buy" amendment would have blocked people on a terrorist watch list banned from flying while under investigation from buying a gun. The measure would also have empowered the attorney general to prevent a gun purchase if there was "reasonable belief" the person could use the weapon for terrorism.
Republicans blocked a similar measure last year.
Cornyn's amendment would have allowed the attorney general to delay a gun purchase for up to 72 hours by a suspected terrorist or a person investigated for terrorism in the last five years. A court order could also have been sought to prevent the sale.
Senate aides believe there could be room for compromise by extending the review period for those previously on the watch list who were later removed.
Dueling amendments on improving background checks for gun sales echoed debates of years' past when, in the year following the shooting massacre at Sandy Hook Elementary School in Newtown, Connecticut, a bipartisan bill on background checks failed.