The NM scholarships in the list in reply #1 includes some competitive ones.
There are also this list here of competitive full tuition to full ride scholarships (not necessarily NM):
http://talk.collegeconfidential.com/financial-aid-scholarships/1461983-competitive-full-tuition-full-ride-scholarships.html
However, assessing the chances of a competitive scholarship is often more difficult than assessing the chances of admission, due to much less public information about the selectivity of competitive scholarships.