HELP - I'm running out of time, and everything is WET

Throw some plywood over it and rolled roofing. You can use Black Jack on any spots water weeps past. The plywood can be reused for other projects and a roll off comp roofing should be cheaper than high quality tarps.
Otherwise, plywood and 10mil or heavier plastic. Staple it past the opening so water doesn't leak, or Black Jack the staples.

Instead of plywood, fiberglass corrugated panels are much lighter and probably cheaper.