Usually this is caused when the motor speed resistors burn out. I would have to look at the serv manaul but most cars now have a resistor card or a electronic board, with resistors soldered to it. It is screwed into the HVAC module and then has an electrical connection. Usually easy to replace and found under the passenger side dash above your feet.
This is what I suspect and have the GM serv manual procedures in front of me, easy to do. IM a fax number and I can fax it to you, I cannot email it. There is a blower relay but if that failed you would get no speeds what so ever. High speed is always there since it is getting full power and when the resistor card goes bad, it defaults if you want to call it that to high only. High speed uses no resistor (full 12 volts) and it is like a safety so you always have a speed to clear the window or move air. Usually not expensive to repair if done on your own.
Funny you mention it, but just before I recently got rid of my '01 Cavalier, the same issue arose with that. The good responses above confirm that it was in fact the blower resistor gone bad. Keep us updated on the repair progress and resolution.