The agency wanted spacewalking astronauts to tackle the job Friday but had to push back the outing to Saturday to give officials on the ground more time to fine-tune the repair plan.
On Thursday, the astronauts aboard the linked shuttle-station put together a makeshift brace for the torn wing, using short strips of aluminum and tape.
"There's advantages to being raised on a farm," said the space station's Iowan-born commander, Peggy Whitson.
They planned to take a break later in the day to speak with former President Bush during his visit to Mission Control.
The solar panel tear is the more pressing of two major issues hampering power production on the orbital outpost. A rotary joint that controls the solar wings on the opposite side of the station is also causing problems.
Both issues threaten to disrupt future construction work at the station, including the planned December launch of a European lab.
But ignoring the wing damage could have even more troublesome consequences. If the damage worsened and the panel lost all power-collecting capability and became unstable, the wing would have to be junked, said Mike Suffredini, NASA's space station program manager.
The wing ripped in two places as it was being unfurled Tuesday, and a hinge may have been yanked and partially ripped.
Engineers suspect the wing became snagged on a support for one of the wing's guide wires, Suffredini said. They do not want to reel it in to make it easier to access for spacewalkers, for fear it could be further damaged.
The torn section of the wing cannot be reached with the space station's 58-foot robot arm. So NASA plans to attach the shuttle inspection boom to the robot arm and put astronaut Scott Parazynski on the boom to free the snagged part of the wing. There would be no need to mend the tears.
Either the wing or joint problem will need to be resolved before shuttle Atlantis can lift off with Europe's lab, which is currently scheduled for Dec. 6.
Suffredini said he and others will figure out what to do about the joint once Discovery undocks from the space station. The shuttle is scheduled to undock on Monday and land on Wednesday.
Touchdown now is slated for early afternoon, as opposed to predawn. As a result, the astronauts will start going to bed a little later each day, between now and then. NASA made the change, in part, to ease the astronauts' schedule, which has been hectic ever since they blasted into orbit Oct. 23.