I just finished it and at the very start the hologram message thing makes it clear that you have a time limit of 1:40 to meet his demands.
Then on the alien planet he contacts you again and seems to show a time left, for me it was 10m and something left which approximately seems to fit in with the amount of time I have registered on Steam.
OK, update. I left the game running and nothing happened, but since the next time you see the countdown is at the end of the game I think it is likely that running out of time might only affects the ending.
Either that or the countdown pauses when you are snoozing or it has no effect at all.
Last edited by BrownEyedTigre; 07/08/14 07:08 PM. Reason: combined stacked posts