There are lots of interesting suggestions here: http://www.linguee.fr/anglais-francais/traduction/time+is+running+out.html I'd be as interested as you are to see which ones a native Francophone would approve of.

J'ai une préférence pour "Le temps presse". Je dirais aussi "Le temps (me/nous...) manque", le temps file...

on n'est pas de temps ? that's the first one come to my mind waiting for a better answer