Smile and congratulate your niece for getting into such a prestigious school and then offer your $100.00 gift for all her hard work. As others have mentioned, even most parents don't help pay for their kids tuition once they hit college age and she should be so lucky.
You are in no way obligated to help her pay and I wouldn't feel the slightest bit guilty about turning her down flat. Why? Because she can attend many, many, many schools well under the student loan and grant amounts she can get own her own without a cosigner and without passing a credit check. (5,500 her freshman year.... more if she is low income). Don't let her fool you, you can ALWAYS change your plans. I'm sure she isn't the first one to try to attend that school who's finanicing fell through. The community college she lives closest to will have open admissions and classes start at many times of the year anymore.
For some reason kids just seem to think money is going to start falling from the sky when they apply to these "prestigious" schools. HA! It is so much easier to spend someone else's money.
You are doing her a favor, if she can't come up with the money this year, but somehow scrounges it out of YOU.... she will be back next year wanting even more... and then again the next year... when you can no longer afford it, she'll blame you for her having to drop out a junior with her own student loan debt because I'm sure she is still borrowing that 5,500 per year in federal loans she can get.
This is forcing her to be a bit more Realistic and is a part of growing up and moving to adulthood. Like I said, it is so much easier to spend someone elses money.
I'm sure she's going to major in something totally non-income earning anyway... lets see, fashon design, YUP... that's my guess. After 4 years with a degree in that, she'll be working at WalMart in the clothing department after atttending that expensive school, in debt and earning about 11 dollars an hour.