Most 737s are just fail passive, as said above. The fail operational 737s can actually do a successfull autoland and automatic rollout if one generator fails below alert height (200ft). They can also do a fail operational autoland to CAT IIIa minima on one engine provided the APU can be started and is powering the other bus.
Putting it another way, for the fail passive aircraft (the majority of all 737s) the fall back is the pilot. For the fail operational aircraft it is the other autopilot, however only below the alert height. Above that it is the pilot. And for those using the HUD only and not any autoland capability it is the pilot to begin with that is doing the low vis landing and the fall back as well.