A mezuzah case is really only a way to extend the halachik doorpost such that there is no need to actually insert the klaf into the doorpost itself, so inherently, size should not be a halachik issue. Even with regard to the mezuzah klaf (parchment) itself, as long as it can fit in the appropriate place on the doorpost (bottom of top third, not within the uppermost four inches**), there shouldn't be a problem (though you might need a rather wide doorpost as well to angle it for the Ashkenazic custom):
** See, however, here (184) which cites that while Rav Ovadia Yosef ruled that it must always be in the top third, traditional Ashkenazic custom, apparently based on a Talmud Yerushalmi, is to put it at shoulder height even when the doorway is much taller.