It's true that the People are themselves above constitutions and laws, but it wasn't in that capacity that Lincoln and the Union States claimed to act, but under color of the authority of the Supremacy Clause of the Constitution. It was in the name of that clause that Lincoln declared insurrection (unconstitutionally) and summoned the State Militias (unconstitutionally). But if you're lying your ass off, you'd better lay a string of whoppers as fast as you can to keep the parade moving. Kinda like the Clintons.
U.S. Const., Art 4, Sec 4: "The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence."
Lincoln carefully stopped quoting from that section before he reached the part that required, as a condition precedent for applicability or action, an "Invasion" or an "Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence."
There was clearly no "Invasion" of the North.
There was clearly no "Application" by the Legislature or Executive of any State.
The Army of the Potomac was not headed South to assist the marshals of the courts in putting down "domestic Violence."