Although I've been sorely tempted to try out some unsavory methods of getting my work done in time for a couple classes, I've really found that talking to the professor to be a much easier, less anxiety-ridden solution. You don't even have to invent personal reasons, at least in my experience. They've been in college, they know the drill. College teaches you time management at least as much as it teaches anything else, and lots of students discover that, at first, they're not very good at it.
In any case, yeah, I'd suggest just talking to the prof. It helps if you've been an active student who already has some sort of relationship with the professor (ie. stopping by their office for help and/or a chat). I know that, for me, I was very daunted by all those black and white deadlines on my various syllabi during crunch time at first. It took me a little bit to find out that those can be more flexible than you'd think at first.
I'm not saying that one should constantly do this, but as a one (or possibly two
) time thing, it's not a big deal. Hopefully you'll learn to manage your time better in the future from this ordeal.