Effect of a bad Air Pump

I have a 2001 VW Jetta 1.8T. The problem with my car is that every time I start it up in the mornings, or whenever it's cold, it makes a loud screeching sound for about a minute. During that loud noise, I'll have to wait till it stops because the brakes won't work. However, as soon as the noise stops, the car works perfectly. I know it has to do with an air pump not working and that it's not so urgent to get fixed. But I was wondering for how long could I have it like that, without it causing any additional problems? I've made so many expensive fixes on my car that I don't want to be doing any more that aren't too necessary. However, I don't want one unresolved problem to create more pricey problems.