A constitutional Republic.
Constitutional because to remain legitimate it had to adhere to the Constitution which defined what "we the people" and the States allowed the federal government to be and how to act. Of course, a lot of that has become muddled over the years through "creative lawyering" and word redefinitions - sort of like an ink blot. You see in it what you want to see.
A Republic because the people did not directly elect all the politicians. Early Senators were appointed by States. The President even today is officially elected by the Electoral College, not the popular vote. Voting members to this college are appointed by the State governments. Of course, most of the time they agree with the popular vote so people forget about them.