I am going to coin this user246's First Law of Testing: everyone who tests software will eventually need to test something with a deadline. (I'm sure several hundred thousand other testers have coined the same law.) Although the specifics vary from one problem to the next, there are two essential solutions: either change the clock or change the deadline.
Changing the clock
The most obvious way to change the clock is to literally change the operating system's definition of the current time. This is risky because there are probably other systems running on the same machine that will behave incorrectly if you change the system time.
The risk is lower if you run your software inside of a disposable virtual machine, i.e. a VM that you plan to destroy when the test is over. However, some VMs (e.g the Xen hypervisors in Amazon EC2) synchronize the VM clock with the host's clock no matter what you do, so this option may not be available to you.
Of course, unless you are testing an operating system, changing the operating system's time is just a way to change an application's definition of time. Sometimes a developer will have the foresight to provide a way to override the application's definition of time. Using this feature probably requires that the tester be able to restart the application.
Changing the deadline
If you can't change the clock, you may be able to change the deadline. Sometimes a developer has the foresight to provide a way to override deadlines. There may be a way to override the deadline when it is calculated; for example, if the trial membership is supposed to last 7 days, there may be a way to force the trial membership to last 5 minutes instead. If you can't override the deadline before it is calculated, there may be a way to change the deadline after it is calculated via a database query or a special web form or whatever.
Your developers may know of a way to do this
Most of the techniques for testing a deadline require special testability features. These features are not necessarily easy to write, and you won't get them by default. If it's hard for you to test deadlines, it may be worth asking your developers for help or advice.