White House spokesman Jay Carney told reporters that President Barack Obama was looking forward to seeing Giffords and her husband, retired and Navy Capt. Mark Kelly, later Wednesday.
He said everyone at the White House was "heartened" to see her appearance before the Senate Judiciary Committee.
The former Arizona congresswoman spoke briefly and haltingly at the beginning of a Senate hearing on tougher gun laws. She urged lawmakers to "be bold" to pass laws to protect children.
Kelly testified as well and described his wife's struggles to walk, talk and see since being shot in an assassination attempt two years ago that left six others dead.