I suspect the opinion in the South about popular sovereignty was divided. Was the New Orleans paper you saw the Picayune? The Picayune opposed secession in the fall of 1860 but later supported it completely.
Here is another opinion on popular sovereignty (or squatter sovereignty, as it was called in the South), this one from the Austin, Texas State Gazette of May 21, 1859. The State Gazette was pro-secession, and it contained numerous articles about slavery, the price of slaves across the South, the possibility of opening up slave importation from overseas again, etc. Its editor was the head of the Democratic Party in Texas.
The principle of Squatter Sovereignty allows any number of men who can first reach a U. S. Territory to set up for themselves and establish their own political institutions. If this principle were true and identified with the spirit or letter of the Constitution, it would be fatal to the South, for it would enable the populous free States to command the settlement of every future territory in existence. But it is a false as well as meretricious theory. A territory is not a mere nullias fillias -- a bastard birth. It is the offspring of the States; it is subject to their authority; it has its period of minority and majority.
Congress stands as agent for the States. It can not only prescribe the rule when it shall come into the Union, but give to it its organic law and government machinery during minority, and command that its law shall be obeyed; and while it may not force slavery upon the territory or prohibit its introduction, any more than any other kind of property -- what it cannot do the territory cannot do, while Congress has the power and must exercise it whenever demanded, to prevent the territory from destroying slave or any other property by contemptuously and vindictively refusing to give it adequate protection.
Thus stands the Democracy of Texas as a conservator and guardian of inalienable rights under the Constitution. The doctrine of squatter sovereignty is calculated to overturn all this. It concedes the right of a body of men to make a government for a territory without consulting the authority of Congress. They may do what they please. The moment that this power of Congress is withdrawn, the squatters of a territory though they be but half a dozen in number, would have a greater power than Massachusetts. They would draw their power from a source above the Constitution ...