The simple fact is that as an employee you should be looking out for yourself. Period. That means pushing back on a hard deadline that will exclude you from trying to get your dream (or simply preferred) job.
If the company won't budge and you're unsure of your prospects then yes by all means accept it, go to the other interview and, if you get it, bail on the other one.
For those that object to this on ethical grounds, consider this scenario: the company has their preferred employee who passes on the job and then they offer it to you. If that first guy comes back and changes his mind, will the company say "oh sorry, we've offered it to someone else". They might. Or they might not (and I've had it happen where they haven't).
If your "safety employer" is a large company don't even give it a second thought. Microsoft or Yahoo will offer hundreds of jobs. Not everyone is going to show. It's factored in and the companies won't die if you don't show up.
Be more careful when it comes to small companies but, as others have noted, smaller companies may be in a situation between getting 0 employees and getting 1. That's a big difference from getting 199 or 200.
Ultimately though, the company's problems aren't your problems, particularly if they exploit your inexperience and relative lack of negotiating power to force you into making a premature decision. That company will have interviewed other people. It will simply extend an offer to the next person on the list.
If they can't get someone to join them they're either not offering enough compensation or they're simply not desirable employers. Neither of which is your problem.