What are the basic principles of a republic? You could have variations, but historically Americans have tended to follow Madison in Federalist Papers #39:
...we may define a republic to be, or at least may bestow that name on, a government which derives all its powers directly or indirectly from the great body of the people, and is administered by persons holding their offices during pleasure, for a limited period, or during good behavior. It is ESSENTIAL to such a government that it be derived from the great body of the society, not from an inconsiderable proportion, or a favored class of it.... It is SUFFICIENT for such a government that the persons administering it be appointed, either directly or indirectly, by the people; and that they hold their appointments by either of the tenures just specified....
Thus a republican form of government takes the government only to be able to exercise its powers insofar as it derives them directly and indirectly from its people, and only exemplified in cases where those administering the government in any of its powers get their appointment from those people.
I would argue on the basis of this that the National Popular Vote Interstate Compact is in fact a violation of the principles of republicanism; that, because of this, Congress has the authority to overturn it if it ever is completed; and that, in fact, Congress has the constitutional duty to do so. While states do have the right to determine how to allocate their electors, the United States has the constitutional duty to guarantee that they do so in a form consistent with republican government.
Under the NPVIC, the electors for the state would be chosen not on the basis of decisions made by the people of that state, but on the basis of a number obtained by adding official popular vote totals from all the different states. This means that the electors are chosen not because they represent the people of the state but because they represent an abstract assessment of the nation, and this abstract assessment is not only based on considering the rest of the nation as more important than the people of the state that the electors are supposed to represent, it is, because state election laws are different, obtained in a way inconsistent with the will of the people of that state, expressed in their election laws, as to how votes should be handled. The appointment of the electors for a state under such a compact is neither a direct nor an indirect expression of the people. The whole point of the Compact, in fact, is to sever the appointment of electors by a state from the expressed will of the people of the state.
Similarly, states assigning electors according to the NPVIC are assigning them on the basis of a process that cannot be directly affected by the people and that cannot be adequately monitored, reviewed, and corrected by their representatives. The people of Colorado have no direct say in the election laws of Connecticut, or of any other state than their own. The elections in different states are monitored, reviewed, and corrected only by the governments of those states, so representatives in Colorado do not have the authority or ability to guarantee that everything in Connecticut is being done in accordance with the will and interests of the people of Colorado. There are, in fact, only two ways to appoint electors that do not sever the appointments from the direct or indirect control of the people of a state: by appointing on the basis of the votes of the people of that state, according to election laws determined by the state legislature; or by the specific deliberation of those who represent the people of that state, according to election laws determined by the state legislature. Neither of these occurs in the NPVIC scenario: the appointment of electors in the Compact is not based on the popular vote of that particular state, but on a number, to which the state popular vote is only an easily swamped contributor. Nor does the appointment involve any specific deliberation by the legislature as to what will best represent the interests of the people of that particular state. The Compact amounts, in fact, to a complete refusal to recognize the electors as representatives of the people of that particular state.
NPV is a bad idea simply on its own merits -- its advocates are unrelenting liars, it solves none of the problems it purports to solve, it is incapable of providing any of the things its advocates promise, and it is based explicitly on the incoherent motivation of treating the normal functioning of the Electoral College as bad while not doing the appropriate thing to fix it (namely, Constitutional amendment). But it is more than that; it is a betrayal of republican principle. And, I would suggest, should be regarded by everyone as unconstitutional.
