"I don't know how many times in your life you ever get to do a ticker-tape parade, but this is beyond anything I ever thought would happen," Glenn said before the parade.
The 77-year-old Glenn, wearing a blue flight suit and seated next to his wife, Annie, perched on a convertible for the ride up Broadway. The celebration came 36 years after he was given his first journey up the canyon for being the first American in orbit.
"I'm just glad to see this outpouring of feeling for this particular mission," Glenn said. "I wish this kind of attention was focused on every flight."
CBS News Correspondent Randall Pinkston reports that the police officer driving the car up Broadway was Thomas Hamilton, who was born 10 years after his father performed the same job for Glenn 36 years ago.
Asked about his own moment in history with Glenn, Hamilton said, "He's a legend and now I'm going to be driving him."
A light flurry of shredded paper greeted Glenn and his crew mates from the space shuttle Discovery crew mates as they made their way past a lunchtime crowd standing about five to seven people deep.
Joining Glenn in the parade were the other shuttle crew members (Cmdr. Curtis Brown, Steven Lindsey, Scott Parazynski, Stephen Robinson, Pedro Duque, and Chiaki Mukai) and their families.
There were fewer people on hand than for some of the city's previous ticker-tape parades. This was the third ticker-tape parade since October; the others were for Chicago Cubs home-run hitter Sammy Sosa and the World Series champion New York Yankees.
It was also the second parade in less than a week for the shuttle crew. Last Wednesday, thousands lined the streets of Houston to honor them.
Glenn launched the festivities Monday morning by unveiling the 20-point, Moravian-style star that will stand atop this year's Rockefeller Center Christmas tree.
Recalling his first parade, on March 1, 1962, Glenn said at the unveiling: "It was just so enormous. I remember just a blizzard of paper. You could hardly even look up without getting something in your eye."
Monday, however, ticker-tape, the paper ribbon on which telegraphic tickers printed information, is no longer used. Participants now throw shredded computer paper, confetti, and toilet paper rolls.
Glenn, who retires from the U.S. Senate next month, is not the only one honored with more than one ticker-tape parade. Others include the New York Mets and New York Yankees, former Ethiopian emperor Haile Selassie, Dwight Eisenhower, and Amelia Earhart.