there could be a number of things that it could be. i'm no expert though, but i would definitly check the spark plugs. it sounds stupid, but it could even be that your plugs could have become fouled, which would make it difficult to start, but if you let it sit overnight the excess fuel won't be on the plugs anymore. that is one possibility because i'm kind of trying to compare it with my bike. it fouls the plugs, if it is running too lean, and i can wait overnight and it will start up fine. i don't know if these are anything alike but that is the best thing i can think of.
the other thing that it could be is if you run your car almost to empty before filling it up, you could suck up any water or debris that could be in your tank that would get into your injectors and clog them. that would stall the engine and make it not be able to run unless you hold the gas down which would try to force the gas, debris, and water into your engine making it harder to stay running. but if sat overnight, it should clear out and be able to run in the morning.
i hope that some of this was helpful! but those are only my guesses, i'm not an expert!