Most of the GM cars I mess with have a "high blower speed relay" on the firewall. There is a separately fused feed from the fuse block to this relay. If the fuse is blown, or if the relay is bad, when you put the switch in "high" you get all the blower resistance in series with the motor, resulting in the blower feeling like it's on "low." I think that's what you mean by "low, medium, and low."

The relay looks just like a horn relay, but it has different connections. On all but one car, it's been on the engine side of the firewall, mounted right next to the A/C box. (The exception was actually a 71 Chevy truck, where it was tucked up under the dash.)

If the relay is mounted under the hood (which it probably is), corrossion can also cause connection problems. Try spraying the terminals with WD-40 if they look questionable.

Good luck!