2004 Chevy Trailblazer Compressor going out

Air Conditioning problem
2004 Chevy Trailblazer 6 cyl Two Wheel Drive Automatic

I was told my AC compressor is going bad. If I wait until it completely shuts down is there a chance of doing further damage that could be avoided by having the work done now? It is still blowing cold air but making whining noise and computer diagnaostics show this to be the problem.