If you had the compressor or bearing freeze up and spin the belt, then that is a problem....you may need to replace it. However, if the compressor just fails to engage, it is likely due to the protection of the triple pressure switch sensing low refrigerant/oil. The refrigerant system also has oil in it for lubrication (not engine oil). Any good A/C shop can examine your system and most will diagnose for free (or a small charge), hoping to get the business. If yours emitted smoke when the compressor stopped, it was likely the belt that got smoked, due to compressor pulley bearing seizure. Your can have the bearing and clutch set replaced if this is the problem.