My 07 Passat AC doesn't blow cold air. Is it possible that the blower motor could be bad?

If you turn on your heat or A/C to high and you get plenty of air blowing out of your vents, it's not the blower motor. If you turn on your A/C and turn it to max cold, and all you get is warm air out of the vents, you have an A/C issue. Bad condenser, low on coolant, etc. You should take it to a certified A/C specialist.

Forgot to mention, try replacing your A/C relay under the hood first. That could be your warm air issue. If not that simple, I would take it in for service.

Find another mechanic. Otherwise ditto on Reelin68's post, just also could be clutch on compressor not engaging, (and that could be the relay he mentioned or the clutch it's self)... leak of R134a, but I would not trust a mechanic that told you the blower is bad.