It is possible to come while not fully erect.
It is also possible to be highly turned-on, but not erect. It's not common, but if you are oversexed enough its possible that even into the next day, you will still want sex, but be unable to perform. If a guy has eaten well, gotten good rest, and not had his brains completely fucked-out in the last day or two, he should be as hard as a rock. Probably the only other possible issue would be hormone related (i.e. steriod crash), but I'm pretty sure libido goes with that too.