"We are confident that she is going to come back to help us full time," Rep. Debbie Wasserman Schultz, D- Fla., chairwoman of the Democratic National Committee, told CBS.
Giffords is still recovering from nearly fatal brain injuries suffered when she was shot in Tucson Jan. 8.
"She is remarkable. Her recovery has been miraculous," Wasserman Schultz said, while acknowledging her friend "still has a long way to go."
"She still has intensive rehabilitation, physical and occupational and speech, and she's working hard. In fact, she went right back to Houston, and she'll be back in all her therapies tomorrow," Wasserman Schultz said.
Giffords received a standing ovation from both parties when she surprised the House by showing up for Monday night's vote on the debt ceiling.
Minority Leader Nancy Pelosi, D-Calif., hailed her as the "personification of courage."
Wasserman Schultz said the party would help Giffords seek re-election next year if she chooses to run.
2014: The Year in Music [PHOTOS]