There is nothing in the text of the Constitution to suggest that it is a treaty among independent nations, and the right to secession shows up nowhere. You don’t need to embrace Lincoln’s robust nationalism — he thought the Union had existed prior to the Constitution and the states, and argued that “perpetuity is implied, if not expressed, in the fundamental law of all national governments” — to reject nullification and secession. You need only go to the Father of the Constitution, James Madison.
Madison held something of a middle position. He explained in Federalist 39 that we have “neither a national nor a federal Constitution, but a composition of both,” or, as he said elsewhere, “a new Creation — a real nondescript.” That didn’t mean that the union wasn’t a nation. “What can be more preposterous,” Madison asked, “than to say that the States as united, are in no respect or degree, a Nation, which implies sovereignty; altho’ acknowledged to be such by all other Nations & Sovereigns, and maintaining with them, all the international relations, of war & peace, treaties, commerce, &c.” In the 1869 case of Texas v. White, the Supreme Court nicely stated a Madisonian view of the question: “The Constitution, in all its provisions, looks to an indestructible Union, composed of indestructible States.”