I expect more Republicans to get behind this as times goes on, for the same reason I expect to see more Republicans get behind single payer healthcare:
It benefits middle class and upper middle class White people, who are the Republican base.
Most minorities already have the opportunity to get a government funded bachelors degree via Pell Grants.
Now middle class Whites (and the smaller groups of middle class African Americans and Hispanics) will be able to get free college as well.
I'd venture to guess most upper middle class whites won't avail themselves of this.
There are "social capital costs" to going to a community college for two years and transferring to a four year-school. It's considered a negative when applying to graduate programs; many top-tier universities generally don't take many transfer students in general; people who rush fraternities and sororities generally do so as freshmen and sophomores; doing things like studying abroad for a summer term are more difficult to do. You'll still get a college degree, but you won't have many of the "soft signalers" that upper-middle class white people care about.