House Democratic leader Rep. Nancy Pelosi, D-California, called Giffords a "bright star" whose "message of bipartisanship and civility is one that all in Washington and the nation should honor and emulate."
"She will be missed in the House of Representatives, but her legacy in the Congress and her leadership for our nation will certainly continue," Pelosi said in a statement.
Republicans also expressed their appreciation for Giffords.
"We salute Rep. Giffords for her service, & for the courage & perseverance she has shown in the face of tragedy. She will be missed," tweeted House Speaker John Boehner.