Could you apply for a deadline extension possibly? My school lets you do that if you have extreme circumstances (like yours). In the meantime you might want to check the newspaper classifieds to see if there's any way you can make a hundred dollars or so in a really short time. You might be able to find some place that does product testing and needs guinea pigs, for example... those are good if you need some quick cash. Or maybe a focus group of some kind, in your area?
You might also consider applying for a credit card, which is a bit easier to get ahold of than a federal grant, or a bank loan. Those kinds of things will cost you in the long run but they're good for meeting deadlines.
I don't really know how these things work in the states, so some of my suggestions might be a bit impractical. Your mother might be able to pull out some money temporarily that you'd have more time to reimburse her for, if she has a credit card or anything of the sort.
Good luck with everything, though. I know how you feel, seeing as I'm saving up for my tuition as well and only have a couple of months to scrape something together.
"God becomes as we are that we may be as he is." ~William Blake