Oh my!
I'd just be upfront and honest with her.
Tell her that now is not the time for you to be taking in any sort of borders. Tell her you are sorry for her woes, but she'll have to find lodging/housing somewhere else.
I know it's hard to turn family/friends away when they are down on their luck, but sometimes you just have to put your foot down and say no. Don't beat yourself up for it. I know you will, because I would do the same thing. I'm a sucker too...have taken in tons of people who needed a place to stay because of hard times. Can't do it anymore. Too much stress on me and too much of a disruption to my life.
***ok, maybe a quilter or 2 staying for a while wouldn't be a bad thing. :) :) :)***