The answer to this differs depending on whether you are in a developer or tester role. I'm answering for the tester role since your other thread indicates that is your role.
I can think of a few techniques:
1) Is it a defect fix release? If so, ask what functionality change. Or ask to see a "diff" report of the code and look yourself (if you are qualified to do so)/
2) Triage - talk with whomever decides these things which parts they want tested given the time constraint.
3) More testers. Granted most testing requires knowledge of the app, but you can always use someone to bang away and explore.
4) Look into automated regression testing so you can write tests while the developers are developing and then have them run faster during the critical period.