If it is a broken sway bar it should not hurt to wait a few weeks to fix it.
Sway bars work to stabilize a vehicle during cornering and turning. Up to about ten to fifteen years ago, they were an optional piece of equipment on new cars and trucks.
The only time that a sway bar (if installed correctly) should actually be working is during hard cornering or turning. It does NOT support any weight, effect the steering geometry, or the wheel alignment of a vehicle. If your sway bar is broken, you may hear a popping or rubbing noise during a hard turn or when cornering, but since it is already broken it shouldn't hurt anything.
Most of the time, when they break, it is towards the end of the bar, near the control arm (where it is actually attached to the suspension of the vehicle). It is not a real major repair but don't expect it to be a cheap fix. Front end work on Chevy Blazers is not cheap, especially if it is a 4 wheel drive.
Don't be surprised if when you take it for repairs, that you are told that you also need to replace the ball joints, too. Since they may have to take them loose in order to replace the sway bar, you may as well replace the lower ball joints at the same time (if they are bad) to save from paying the labor twice by waiting to do it later.