I am looking for a free software package which will allow for the
scheduling of resources such as meeting rooms. I realize that there
are many of these out there, but I need one with a specific feature -
each user of the system is to be granted a certain number of hours per
month, and they may not book more than that number of hours.

If you can find a package that has this feature, answer this question,
otherwise, please do NOT answer it. I am currently planning on
modifying http://ors.sourceforge.net/ and adding that feature myself,
but I'd like to same myself some effort if such a thing already
exists.