The one area that Clinton has room to grow is with white women - I would love for her to choose someone like Warren as VP to see if she can eat into those numbers for white women and liberals.
That would definitely help her. I think a lot of liberal women (particularly younger) are sort of meh about Hillary. On the one hand, she could be the first woman president, which is fantastic. On the other hand, there is not much to actually like about her, and she will be a downgrade from Obama on a substantive basis. There is really a huge age divide, with older women much more enthusiastic about Hillary.
If she could do something to turn that meh into actual enthusiasm, she would indeed have room to grow. Picking Warren, or another qualified solidly progressive woman as her running mate, would go a long way.