In a scathing op-ed for The New York Times, Giffords says the lawmakers who voted against the bipartisan gun control package displayed "cowardice."

"Speaking is physically difficult for me," Giffords, who was badly injured during the 2011 Tucson shooting spree, writes. "But my feelings are clear: I’m furious. I will not rest until we have righted the wrong these senators have done, and until we have changed our laws so we can look parents in the face and say: We are trying to keep your children safe."

In the piece, the former Arizona lawmaker accuses "a minority of senators" of bringing "shame on themselves and our government itself by choosing to do nothing" despite public support and lobbying efforts by the victims of gun violence. She also pledges to rally public support against the senators who voted against the bill.

"Mark my words: if we cannot make our communities safer with the Congress we have now, we will use every means available to make sure we have a different Congress, one that puts communities’ interests ahead of the gun lobby’s," Giffords writes.

Earlier Wednesday, Giffords personally visited with senators ahead of the afternoon vote, which fell five votes short of the 60 necessary. She later appeared at the White House with President Obama and victims' families from the Newtown, Conn., elementary school massacre.

At the event, the president offered similar disappointment, saying "this was a pretty shameful day for Washington."

"If action by Congress could have saved one person, one child, a few hundred, a few thousand — if it could have prevented those people from losing their lives to gun violence in the future while preserving our Second Amendment rights, we had an obligation to try," Obama said. "This legislation met that test. And too many senators failed theirs."

Giffords and her husband, former astronaut Mark Kelly, launched a super-PAC earlier this year designed to counter the political influence of the National Rifle Association. The group — Americans for Responsible Solutions — has said it hopes to raise $20 million to spend on the coming 2014 election.