What you're calling the "faucet" is the tub spout. Thus, you have a tub spout diverter.
I believe that is where the problem lies.
Remove the tub spout diverter and see if you have normal pressure coming from the stub-out (the pipe that the spout is connected to).
Look for a hidden set-screw. If you find one, you'll need the correct allen wrench to unscrew it. Then pull off the spout. If there's no set screw, you can unscrew the spout using a large channel locks with a rag underneath (to avoid marring the surface).