The Federalist Papers actually have a very powerful argument (#22) against the thing that's most problematic with EC:

"Every idea of proportion and every rule of fair representation conspire to condemn a principle, which gives to Rhode Island an equal weight in the scale of power with Massachusetts, or Connecticut, or New York; and to Deleware an equal voice in the national deliberations with Pennsylvania, or Virginia, or North Carolina. Its operation contradicts the fundamental maxim of republican government, which requires that the sense of the majority should prevail. Sophistry may reply, that sovereigns are equal, and that a majority of the votes of the States will be a majority of confederated America. But this kind of logical legerdemain will never counteract the plain suggestions of justice and common-sense. It may happen that this majority of States is a small minority of the people of America3; and two thirds of the people of America could not long be persuaded, upon the credit of artificial distinctions and syllogistic subtleties, to submit their interests to the management and disposal of one third. The larger States would after a while revolt from the idea of receiving the law from the smaller. To acquiesce in such a privation of their due importance in the political scale, would be not merely to be insensible to the love of power, but even to sacrifice the desire of equality. It is neither rational to expect the first, nor just to require the last. The smaller States, considering how peculiarly their safety and welfare depend on union, ought readily to renounce a pretension which, if not relinquished, would prove fatal to its duration."

"But this is not all: what at first sight may seem a remedy, is, in reality, a poison. To give a minority a negative upon the majority (which is always the case where more than a majority is requisite to a decision), is, in its tendency, to subject the sense of the greater number to that of the lesser. Congress, from the nonattendance of a few States, have been frequently in the situation of a Polish diet, where a single VOTE has been sufficient to put a stop to all their movements. A sixtieth part of the Union, which is about the proportion of Delaware and Rhode Island, has several times been able to oppose an entire bar to its operations. This is one of those refinements which, in practice, has an effect the reverse of what is expected from it in theory. The necessity of unanimity in public bodies, or of something approaching towards it, has been founded upon a supposition that it would contribute to security. But its real operation is to embarrass the administration, to destroy the energy of the government, and to substitute the pleasure, caprice, or artifices of an insignificant, turbulent, or corrupt junto, to the regular deliberations and decisions of a respectable majority. In those emergencies of a nation, in which the goodness or badness, the weakness or strength of its government, is of the greatest importance, there is commonly a necessity for action. The public business must, in some way or other, go forward. If a pertinacious minority can control the opinion of a majority, respecting the best mode of conducting it, the majority, in order that something may be done, must conform to the views of the minority; and thus the sense of the smaller number will overrule that of the greater, and give a tone to the national proceedings. Hence, tedious delays; continual negotiation and intrigue; contemptible compromises of the public good. And yet, in such a system, it is even happy when such compromises can take place: for upon some occasions things will not admit of accommodation; and then the measures of government must be injuriously suspended, or fatally defeated. It is often, by the impracticability of obtaining the concurrence of the necessary number of votes, kept in a state of inaction. Its situation must always savor of weakness, sometimes border upon anarchy."

Hamilton wrote it about the one-state-one-vote arrangement under the Articles of Confederation, of course. But the arguments themselves are clearly very much applicable to the current situation in the Senate and EC.