Four amendments - two Democratic and two Republican - were introduced and received votes. All four failed to pass the 60-vote threshold necessary to advance in the Senate.
The legislation was accelerated last week when Senator Chris Murphy staged a 15-hour marathon Senate speech pressing for common sense gun control in the wake of the attack on a Florida gay club that left 49 people dead.
Murphy's amendment, which would have expanded background checks for individual gun sales to include those conducted at gun shows or online, failed to clear the procedural hurdle, going down 44 votes to 56.
A Republican measure expanding funding for the background check system also failed to advance, as did a Republican effort to authorize court orders that would delay gun sales by 72 hours for people on terror watchlists or "no-fly" lists to allow authorities to investigate the would-be purchasers.
Democrats had felt that the measure was not restrictive enough.
The fourth defeated measure, by Democrat Dianne Feinstein, would have prevented gun sales to people featured on "no-fly" terrorism screening lists.
Senator Bernie Sanders, who is running against Hillary Clinton for the Democratic presidential nomination, said the Democratic measures were "no brainers" and common sense efforts to reduce gun violence.
"It is incomprehensible to me, and I believe to the vast majority of Americans, as to why Republicans would oppose them," he said.
"We have got to do everything we can to stop guns from falling into the hands of people who should not have them."
