Whether or not she's obligated, she has the upper hand, Ed. Your squatters rights may well buy an extra two months, but if she wants you out, she is going to win... full stop. I suggest that you try to appeal to her kindness (I'm in a similar boat, so I speak from experience), and make plans to move on. The cost of doing so will be trivial when compared with the legal fees you would incur by suing her.

As far as my situation is concerned, my landlady also wants to sell, but I explained to her:

1) I have 10 years worth of accumulated crap there, which would be annoying for her to dispose of
2) The apartment is not in a presentable condition for prospective buyers
3) Even if it was, I would not let them in as long as I'm paying her
4) If she boots me, her revenues drop to zero
5) I am nice (a de facto grandson)

Net result... two month extension.