I don't know if it is too late. I mean it is cutting it really really really close, but if you know a professor and did well in his/her class ask him/her. Also, if you don't mind not being paid tell, them that too. I know when I told that to the person I am going to do research for, they were excited to hear that and couldn't wait to get me started. It really depends on the school you go to though and the relationship you have with your department/professors. Hope that helps and don't stop trying yet if you really want to.