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. According to Ashkenazic custom you might also need a rather wide doorpost as well in order to be able to angle it. On the other hand, you would not need as tall a doorpost since the Ashkenazic custom is to place it at shoulder height if the doorway is very tall (see Shach 289:4 based on Yerushalmi; in contrast, see also Yalkut Yosef YD 285:77 who does not rule differently for tall doorways). See: http://www.halachipedia.com/index.php?title=Mezuzah:
** 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.