I will assume you are talking about a stock Q-Jet on a base 200hp, 350cid equipped car. This is a divorced choke carb. the fast idle cam is a weighed (the unbalanced weight cause the cam to drop or go to slow idle as the choke opens) assembly that is operated by a lever on the choke, choke pull-off assembly that is directly connected to the choke thermostat mounted in a well in the intake manifold. This cam would not move for the following reasons:
1 - thermostatic coil not working properly (then the whole choke assembly will not work, see Hib's question).
2 - the choke/ choke pull-off plate was removed and reinstalled improperly. The "tang" that operates the fast idle cam was installed ABOVE the cam. It should fit into a notch in the bottom of the fast idle cam in order to LIFT IT. I have seen this done before and it is easy to do.
3 - the lifting "tang" is broken off the choke bellcrank arm.
So if your choke butterfly is operating correctly (completely closing when cold and opening as the engine warms, then your problem is either #2 or #3. If you by chance have an earlier Q-Jet that used the plastic fast idle cam then I would have suspected the camto have broken just past the fulcrum and thus not engaging the lifting "tang". But I think Rochester started using an all metal cam somewhere about 1969 or '70.
Good Luck,
Mike