According to an article in the Chicago Sun Times, over 500 extras were used for the scene:
Aykroyd remembers a "day of intense concentration'' while working with so many extras -- more than 500, including 200 real soldiers. Belushi hurt his back pushing a cigarette machine and a bench in front of the fake doors, recalled his widow, Judy Belushi Pisano.
If you came upon Daley Plaza on Labor Day weekend 1979, you might have turned and run for cover. Two hundred National Guardsmen, rifles in hand, raced from Army jeeps and tanks toward the Cook County Building. They were backed up by three Sherman tanks, three helicopters and three fire trucks. Not to mention 100 state and city police officers in 50 squad cars and on 15 horses.
There was even a SWAT team crawling across the roof and rappelling down the Corinthian columns of the building.