Giffords sent the same wake-up song to commander Mark Kelly in 2006 when they were just dating.
The astronauts spent the rest of the morning looking for damage to the shuttle's heat shield - a routine procedure started after the 2003 Columbia disaster. NASA said Endeavour looks "really good."
The shuttle is expected to arrive at the International Space Station on Wednesday.
Endeavour is on a 16-day mission - the second to last space shuttle flight and last for Endeavour. Its main mission is to attach to the space station a $2 billion physics experiment: a giant magnet that looks for antimatter and dark energy.
Back at the Kennedy Space Center launch site, Atlantis, which will fly the final shuttle mission of the 30-year program, moved for the last time from its hangar to the massive Vehicle Assembly Building.
Discovery, which flew its last mission in February, had some of its remaining toxic fuel drained from its smaller engines. It will go to the Smithsonian Air and Space Museum hangar outside of Washington's Dulles Airport.
The Associated Press contributed to this report.