Realistically speaking, it's impossible... IIRC, the Shuttle breaks the sound barrier before clearing the launch tower.
Er, what do you mean by 'clearing'? If you mean 'over ten times the height of the space shuttle' (600m), the astronauts would still be subjected to over 10 Gs' worth of acceleration.
Based on
this picture, it looks like the launch tower is less than twice the shuttle's height. Given that, the astronauts would be subjected to over 50 Gs of average acceleration. A 200-lb human would (briefly) experience the sensation of weighing 10,000 lbs, about as much as an elephant, shortly before they became a permanent part of the shuttle's interior decoration.

EDIT: If the space shuttle maintained that acceleration, though, it could reach the speed of light in about a week.
EDIT 3: My mistake, the shuttle would only exert as much force on the launch pad as half of one of the WTC towers. And once it had reached about 80km, still assuming a constant acceleration, it would have released about as much energy as the first nuclear bomb: (2029203 kg*(((343 m/s)^2)/(2*120 m)) *80000 m)/(19*4.184*10^12 J)
Boy would those crowds be sunburned.

EDIT ???: 'course, they probably wouldn't notice, since the shuttle would get there in about 18 seconds: (2*80000 m/(((343 m/s)^2)/(2*120 m))))^(1/2)