I had this issue when I started my Masters in Math. What happened with me is that I, in a discussion about the year, was asked about my funding from her, and I told her I didn't have any, to which in a week later (when someone threatened to make me his student) she gave me a modest portion of her grant to work under her. This next year is my next year, and the Assoc. Head is giving me a TAship since he's now so low on teachers since our university just got the VIGRE grant (2.3mil/3 years, extends to 3.8/5, only research), and we lost so many TAs. Basically, try to stretch the options, really look. I applied for 8 scholarships this year, and ended up getting enough money to do my research in Italy over the summer with another university.
My end advice though is to not jump in without any funding at all...because you don't know how much they care if they don't give you anything.