That could be an "it depends". I can believe a lot of public universities have quotas on CS undergrads (and other majors, especially ones that require labs, and until recently as these things go that was a big issue for CS), but it's the mark of a good private school that if an undergraduate wants to major in X, they'll find a way. CMU is the only exception I know to this, has a quota of about 135 CS students the last time I checked.

According to this page http://www.statista.com/statistics/183995/us-college-enrollm... , as of 2011 61% of students enrolled in public colleges. That's for students at all levels, however (you can use this page to subtract those, but it's breakdown is by gender: http://www.statista.com/statistics/236654/us-post-baccalaure... ).