Near the beginning of the movie, we know it's February 18, 2014.
Chris: It is February 18th, 2014. My brother has officially lost his mind. He genuinely believes he is building a time machine.
Towards the end of the movie, we find out that it's April 23, 2014.
David: It's April 23rd, 2014. This is to keep a record. I know exactly what to do to fix this. Justin broke his leg at Walker's party. I'll fix that. Everything else will fall into place.
So only about two months elapse from the time they start building the time machine, to when things go off the rails.
From there it's impossible to know how much time passes from David's perspective, because we don't know how many times he goes back, or how long he stays each time. That's left purposely vague.
Jessie: How many times have you done this before? David, how many times have you done this before?