CAPE CANAVERAL, Fla.— NASA was still undecided Sunday when the space shuttle Endeavour might be launched on its final mission. That decision will be made Monday or Tuesday, with the earliest possible launch next Sunday.

NASA sent Navy Capt. Mark Kelly, commander of Endeavour, and his five-man crew back to Houston to wait for the next attempt. Meanwhile, NASA engineers will try to figure out why an Endeavour switch box failed Friday, forcing the launch to be postponed just 3 1/2 hours before it was scheduled.

If NASA cannot launch Endeavour next Sunday, the scheduling gets even more complicated. May 9 is probably not available and May 10 and May 11 would present problems as well, as NASA tries to coordinate Endeavour’s schedule at the International Space Station with that of a Russian Soyuz that is already there.

Kelly’s wife, U.S. Rep. Gabrielle Giffords, D-Ariz., who was wounded in a January assassination attempt but recovered enough to travel Friday to Kennedy Space Center for the launch attempt, returned to her rehabilitation hospital in Houston.

President Barack Obama and his family also attended Friday. It was unclear Sunday whether they would return for the launch.

“”Unfortunately, we’re not going to be able to make a launch attempt in the next few days,”” said Mike Moses, chairman of the mission-management team. “”I’m here to disappoint everyone by saying I’m not going to tell you what the new launch date is because I have no idea. We have a lot more to evaluate.””

Friday’s launch attempt was scrubbed because a hydraulic system fuel-line heater failed. Officials had hoped the problem was simply a faulty thermostat, and proposed a Monday launch on that chance. But once technicians got inside the Endeavour’s aft equipment bay late Saturday, they realized that the problem originated in a switch box called a load-control assembly. To replace that, engineers have to retest many of the systems that box controls, and those evaluations would take at least a couple of days, eliminating any prospect of a launch early this week.

The latter part of this week is not available to NASA because the Air Force intends to launch an Atlas V rocket from Canaveral Air Force Station, adjacent to Kennedy Space Center, Friday, to carry a satellite into space. That launch eliminates Thursday, Friday and Saturday options for Endeavour.

That leaves Sunday. But Moses and other NASA officials are not yet optimistic about that day, because there is so much yet to evaluate with the switch-box problem.

The next three days become problematic because the Russians are planning to undock their Soyuz spacecraft from the International Space Station about the same time that Endeavour would be undocking, and the two maneuvers will not be attempted on the same day.