While the  American constitution  doesn't say out right that college is a guarantee, the constitution does guarantee democracy and free speech. However, as our country switches from an industrial powerhouse  (like it was when the Public K-12 school came around) - to a more desk job orientated economy and the issues that we deal with in politics move from more simple, (such as the right to union), to more complex (like government surveillance), there is a economic and political need for citizen to be educated.

While originally free education K-12 education came about in America was so that people would be able to grow up to work in factories or run retail shops The few who need college went on to be doctors or lawyers.  Now the best and most in-demand careers all require an education past what is learned in a High School. Even  people who run small businesses or work in a factories now must work with machines and computers that all require education past what can be taught in 12 or 13  years. Free college helps us maintain an America in which people are economically sound. If there are no jobs security, and the economy tanks there is no America for the constitution to apply to.
Another reason for  free college education is the fact the politics have become more and more complex, as fewer and fewer people are able to actively engage and understand them. Politicians have "accommodated" for the general populace by lowering the amount of education need to understand political rhetoric ( see Presidential Speeches Were Once College-Level Rhetoric—Now They're for Sixth-Graders

 However this lack of sophistication that the public is given when talking about politics justs allows for politicians to sweep things under the rug. With recent events like the Flint Water Crisis- which mostly affected underprivileged and undereducated people- as well the openly racist Presidential Candidate Donald Trump, who speaks at a 4th-grade level, it is clear that people need more educations so they can protect themselves from injustice.

Furthermore, as college become too expensive to afford here, we may soon lose our best and brightest to other nationals that offer free college courses in English.

 If we don't act now, there may soon be a shortage of professionals  as people leave the country in search of free education and other benefits, like better health care.

While the Constitution mentions nothing about education, we can not uphold the values of the constitution if we have an unemployed and uneducated populace. Therefore, to remain a viable and powerful nation, we must  join hordes of other developed countries by offering free or reduced post-secondary education