Forecasters said Tuesday that there was a 70 percent chance of favorable weather for Thursday's launch, with a slight chance of showers. Earlier, the chance for good weather had been put at 60 percent. Stiff winds peeling off from Hurricane Mitch are the only concern.
CBS.com will carry a live WEBCAST of Thursday's launch.
Glenn's wife, Annie, expressed fear about the flight, but not as much as the first time around, reports CBS News Correspondent Sharyl Attkisson.
Said Mrs. Glenn, "Back then, it was so unknown, and I was scared then. I am scared now, but not to the point that it is going to take over, that's all. To tell you the truth, he's wanted to go on every flight, and he's always been very, very excited about watching them, and he has kept up on space."
If the launch is delayed for some reason, forecasters said weather could become more of a problem. The outlook for favorable launch conditions declines to 60 percent for both Friday and Saturday.
Glenn and his six crewmates have some rare leisure hours Tuesday at the crew quarters, a short drive from the launch pad.
They were to review their flight plans, check equipment (including their spacesuits), and undergo brief medical exams. In the afternoon, they were given five hours of free time to spend with adult family members. As a guard against colds or infections, mission rules bar children and teen-agers from the crew quarters.
Nearby, preparations by spectators and journalists were reaching a pace that rivaled the frenzy of the Apollo moon shot days of 30 years ago.
Motels in nearby Titusville and Cocoa Beach were filled. Traffic jams were common.
Along highways that afford cross-water views of the launch pad, workers erected barriers and installed portable toilets for the thousands of tourists expected to watch Glenn's return to space. By launch day, the highways are expected to be lined with cars and recreational vehicles filled with spectators awaiting the show.
About 3,500 journalists have registered to cover the mission. More than two dozen television trucks jammed the media complex.
President Clinton and a large congressional delegation are scheduled to attend, along with sports and show business celebrities.
The crew was about an hour late arriving at the space center Monday. One of the five T-38 jets carrying the crew members developed a batter problem when the astronauts stopped for refueling at Tyndall Air Force Base in the Florida Panhandle. Scott E. Parazynski waited at Tyndall for a ride in another plane while the others flew on to the Cape.
In brief remarks after arriving, Glenn introduced himself as "PS2 on this flight." Payload specialist No. 2 is the lowest rank on the crew.
"I am very glad to be here," Glenn said. "I have been pleasantly surprised at the outpouring of interest in this flight, and it's really gratifying to see people get so fired up about the space program again."
Glenn walked quickly to his waiting family, hugging his wife and his children, daughter Lyn and son David. Lyn held her father for a long moment, apparently whispering in his ear.
In an interview earlier in the day, the astronaut's son said he at first was apprehensive about his father returning to space 36 years after becoming the first American in orbit.
Dr. David Glenn, a family physician, said that when he learned of his father's space shuttle flight, he saw mental images of the 1986 explosion of Challenger that killed seven astronauts.
"I just watched it over and over and over," he said.
More recently, though, the doctor said has come to believe that the shuttle safety record "is as close to perfect as you can imagine it possibly being, so I've sort of gotten beyond seeing that replay in my head."
Discovery's nine-day mission will concentrate on science, with Glenn participating in 10 experiments on the effects of weightlessness on the human body and how those effects might relate to aging on Earth.