I have a floor lamp with a three-stage turning switch: off->low->high. I use the lamp only on the high setting, but need to pass through the low setting to get there. It's rated at 150W and I've been using CFL 150W equivalent. The bulb life has been terrible. Do I need dimmable CFLs?
A 3-way lamp has 4 positions: off, low (filament 1), medium (filament 2) and high (filaments 1 and 2). If you are using a standard (non-3-way bulb) instead of being OFF-LOW-MED-HIGH the sequence is OFF-OFF-ON-ON with no ill effect. The bulb simply uses one of the contacts (filament 2) instead of both.
However you say your lamp only has 2 "on" positions, so it's not a standard 3-way lamp then. I think it's likely that there is in fact a built-in dimmer and so yes your CFL bulbs are being burned out by the dimmed fixture. (Some dimmers never actually reach full voltage at "high" so it's possible that the lamp is being dimmed slightly even when on full.)
I would try replacing the bulb with a dimmable CFL to see if that gets better results (or upgrading to a dimmable LED).
As I said in my comment to the original question, turning CFLs on and off frequently can significantly shorten their life so that may be another possible explanation. Again, upgrading to an LED would solve that problem as well since they are not bothered by being switched on and off.
There should be no ill effect from using a standard CFL in a normal three-way lamp; it's just switching another contact, not acting as a dimmer.
Bulb orientation, or heat entrapment, might be concerns. Or there might be something else causing that lamp to run at lower than normal voltage.