The U.S. Constitution carries no explicit authorization for the federal government to have any role in education. Nevertheless, this did not preclude the nation’s first president from advocating the creation of federal civilian and military universities. George Washington made his case to Congress repeatedly, perhaps most forcefully in his eighth presidential address (1796):
I have heretofore proposed to the consideration of Congress, the expediency of establishing a National University; and also a Military Academy. The desirableness of both these Institutions, has so constantly increased with every new view I have taken of the subject, that I cannot omit the opportunity of once for all, recalling your attention to them…. Amongst the motives to such an Institution, the assimilation of the principles, opinions and manners of our Country men, but the common education of a portion of our Youth from every quarter, well deserves attention. The more homogeneous our Citizens can be made in these particulars, the greater will be our prospect of permanent Union; and a primary object of such a National Institution should be, the education of our Youth in the science of Government . In a Republic, what species of knowledge can be equally important? and what duty, more pressing on its Legislature, than to patronize a plan for communicating it to those, who are to be the future guardians of the liberties of the Country?
The Institution of a Military Academy, is also recommended by cogent reasons. However pacific the general policy of a Nation may be, it ought never to be without an adequate stock of Military knowledge for emergencies.
Washington was dispirited by his inability to see his vision into existence. He declared in a 1797 letter,
My Sollicitude for the establishment of a National University in this Country, has been great, and unceasing; but as the Sentiments of the Legislature have not been in unison therewith, I had postponed the further consideration of the subject to a moment of more leizure (than has lately been my lot) to see if I could devise some Plan by which my wishes could be carried into effect.
Washington died two year later. In 1802, Congress established the United States Military Academy (AKA West Point), the first of five national military schools. Congress later established civilian higher education institutions, including Gallaudet (1857) and Howard universities (1867), but it did not create a national university for the study of government as Washington desired. Legislation to establish a United States Public Service Academy was introduced in the 109th through 111th Congresses; none of these bills emerged from committee .
Below are links to four Washington documents that mention his proposal for a national university.
Source: John C. Fitzpatrick, ed., The Writings of George Washington from the Original Manuscript Sources, 1745-1799 (1931-1944), at http://etext.virginia.edu/washington/fitzpatrick/.