What would Alexander Hamilton's opinions on the filibuster be? In short...we can't know for sure. The filibuster did not exist during Hamilton's lifetime (see previous post about its origins).

But in enumerating the defects of the government under the Articles of Confederation, Alexander Hamilton had this to say in Federalist No. 22 about a republican government ruled by a super-minority:

(Historical Context: the Articles of Confederation set up a unicameral congress in which each of the thirteen states had one vote. Bills required votes by a minimum of nine states to be passed and changes to the Articles themselves required unanimous consent by all thirteen states)

The right of equal suffrage among the States is another exceptionable part of the confederation. 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 Delaware, an equal voice in the national deliberations with Pennsylvania or Virginia, or North-Carolina. Its operation contradicts that fundamental maxim of republican government, which requires that the sense of the majority should prevail.

...

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 number. Congress from the non-attendance of a few States have been frequently in the situation of a Polish Diet, where a single veto 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 intire 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 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 controul 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 over-rule 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 savour of weakness—sometimes border upon anarchy.

It is not difficult to discover that a principle of this kind gives greater scope to foreign corruption as well as to domestic faction, than that which permits the sense of the majority to decide; though the contrary of this has been presumed. The mistake has proceeded from not attending with due care to the mischiefs that may be occasioned by obstructing the progress of government at certain critical seasons. When the concurrence of a large number is required by the constitution to the doing of any national act, we are apt to rest satisfied that all is safe, because nothing improper will be likely to be done; but we forget how much good may be prevented, and how much ill may be produced, by the power of hindering the doing what may be necessary, and of keeping affairs in the same unfavorable posture in which they may happen to stand at particular periods.

Read the rest of Federalist No. 22 (1787) by Alexander Hamilton.