To amend the Constitution takes the act of majorities of state legislatures in three quarters of the states. I suppose that is what he meant by "whole people." But the Constitution was not the act of the lumpen mass of people of the whole country. It was the act of the people of the individual states acting through their ratification conventions.
Besides, the Constitution doesn't need to be changed for secession to take place. The withdrawing of a state from the Union was certainly viewed as permissible and consistent with the Constitution by people who actually ratified the Constitution. They had recently gone through a war to win their independence from an oppressive government. Why would they enter an untried form of Union from which they could not withdraw without a war if a majority other states or the central government were oppressing them?
The New York ratification document provides one of the clearest statements of the original intent that a state withdrawing was consistent with the Constitution. That ratification document was voted for by such Federalist luminaries as Alexander Hamilton and future Chief Justice John Jay:
WE the Delegates of the People of the State of New York, duly elected and Met in Convention, having maturely considered the Constitution for the United States of America, agreed to on the seventeenth day of September, in the year One thousand Seven hundred and Eighty seven, by the Convention then assembled at Philadelphia in the Common-wealth of Pennsylvania (a Copy whereof precedes these presents) and having also seriously and deliberately considered the present situation of the United States, Do declare and make known.
... That the Powers of Government may be reassumed by the People, whensoever it shall become necessary to their Happiness; ...
... Under these impressions and declaring that the rights aforesaid cannot be abridged or violated, and that the Explanations aforesaid are consistent with the said Constitution, And in confidence that the Amendments which shall have been proposed to the said Constitution will receive an early and mature Consideration: We the said Delegates, in the Name and in the behalf of the People of the State of New York Do by these presents Assent to and Ratify the said Constitution.
Virginia's ratification document that talked about resuming governance was written by James Madison, future Chief Justice John Marshall, and three other Federalists.
The Union that remained after the southern states withdrew in 1860-1861 did not cease at all. However, during the war the Constitution was twisted into a pretzel by Lincoln.
>> That the Powers of Government may be reassumed by the People, whensoever it shall become necessary to their Happiness; <<
Did that mean?
1. There should be a lawful means by which the People should be able to win redress for their grievances, amend the Constitution as they see fit, and even, hold a Constitutional convention so as to replace the Constitution as a whole when the entire People concur that the new government is failing at its aims of securing freedom
or
2. If anyone subgroup of the People feel so motivated, they can declare that the Laws of the government do not apply to them any longer?
Notice there is no portion of that quote which makes any mention of the State taking action separate from the Nation.
Does the clause reserve the sovereignty of the State of New York, or the People of the State of New York?