There have been quite a few folks that believe that a committed relationship and polyamory are mutually antagonistic. "Oh I don't want poly, I want a committed relationship".
I agree with the earlier post - what they really mean is an exclusivity agreement between them. That is pretty much a centrepiece of a monogamous partnership.
For me, commitment is a set of things that you have agreed to about the relationship (and so doesn't exclude the narrower monogamous definition). It's about not walking away at the first sign of trouble, it's about making an effort to "make things work" when times are rough. It's about having a sense of confidence in the other that you can rely on.
I don't believe that it should be a "one size fits all" thing - different people need and want different things in their lives.
Going back to RP's original post - this "I don't want to tie her down, but I need her to want to be with me more" is a tough one, because essentially it feels like they are wishing that the other person felt differently. Dangerous place to go, in my opinion.
We have to understand our needs, wants and likes, and that includes understanding what we need from the other people around us. If we are to have successful relationships, we have to effectively communicate that with folks, and to find out whether the commitments offered and needed are compatible.
There again, is it possible that this can be ascribed to a lack of communication? Maybe she doesn't know that he wants more time with her, feeling like he "needs his space" when in fact she would like that very much. This could be a bad case of "second guessing" what the other wants, and neither end up getting what they need.
"Listen, or your tongue will make you deaf." - Native American Proverb