In 1776 the idea of a popular referendum to decide this issue would have been very radical. To cast a ballot, a voter had to not only be free and male, but meet a property requirement. In Massachusetts alone , he had to be worth at least 20 pounds and also be determined by a public official to be an inhabitant of the town. Twenty pounds were a year's wages for a craftsman, so this was not a small amount. If you had asked men like John Adams and John Dickinson, they would have said that they were the elected representatives of their states, and that they had been given the authority by their voters to deal with the crisis- Adams being in favor of separating from England, Dickinson resisting it until it was unavoidable.

The newly-written 1776 Constitution of Pennsylvania extended the vote to all free males, in order to reap some popular support, but it was an outlier, something written in the middle of the war: and it was not submitted to the people of Pennsylvania for ratification. And once peace came in 1782, legislatures began to roll back such popular concessions, as there began to be some concern over "mob rule" in the new republic.

By the time of the secession crisis in 1861, however, "mob rule" was no longer feared; there was no longer a property requirement for voting, and the idea of a referendum was no longer radical. So, there was usually a vote in every southern state to determine whether to secede or not. There was often first a popular election of delegates to a convention, and those delegates voted on whether to secede. For South Carolina, the vote by the legislature was clear and the state just seceded. Kentucky's legislature, which was Unionist, avoided calling a convention, fearing that a convention would vote for secession. But for many, like Arkansas, Tennessee and Virginia, there were significant numbers of convention delegates opposed to secession, and a popular referendum was held following the vote to secede. Once Lincoln called up troops in response to the taking of Ft Sumter, southern public opinion swung more strongly towards secession, and the popular votes for secession grew. But these referenda also exposed which areas were Unionist and which were not, and would result in western Virginia almost immediately beginning the process to split off and become its own state, and east Tennessee almost doing the same.

These votes did not change the view of the Unionists, especially Lincoln, that secession was illegal. I quoted his first inaugural address in a recent answer, here it is again:

Again, if the United States be not a government proper, but an association of States in the nature of contract merely, can it, as a contract, be peaceably unmade, by less than all the parties who made it? One party to a contract may violate it---break it, so to speak; but does it not require all to rescind it?

Descending from these general principles, we find the proposition that, in legal contemplation, the Union is perpetual, confirmed by the history of the Union itself. The Union is much older than the Constitution. It was formed in fact, by the Articles of Association in 1774. It was matured and continued by the Declaration of Independence in 1776. It was further matured and expressly declared and pledged, to be perpetual, by the Articles of Confederation in 1778. And finally, in 1787, one of the declared objects for ordaining and establishing the Constitution, was ``to form a more perfect union.''

But if destruction of the Union, by one, or by a part only, of the States, be lawfully possible, the Union is less perfect than before, which contradicts the Constitution, and therefore is absurd.

It follows from these views that no State, upon its own mere motion, can lawfully get out of the Union,---that resolves and ordinances to that effect are legally nothing; and that acts of violence, within any State or States, are insurrectionary or treasonable, according to circumstances.

As for the people in the Union who were sympathetic to the Southern popular vote for secession, they would be in favor of the North making concessions to the South in order to bring them back into the US. That was what the North had generally done before 1861 when the South made threats, and what they and most in the South probably assumed would happen again.

Pole, J. R. (1957). Suffrage and Representation in Massachusetts: A Statistical Note. The William and Mary Quarterly, 14(4), 560–592. https://doi.org/10.2307/1918521