If you check submissions for the previous LOWREZJAM jams, you'll see there were a few attempts at FPS games with 64x64 resolution. Imho the resolution is just too small for any kind of viable 3D game. It's mostly because anything further than a few steps in front of your camera cannot be rendered in a visible manner anymore.
That being said, don't let this descourage you. Please do try it out. You may find workarounds, or come up with gameplay ideas that circumvent this limitation. Good luck!