We've covered this on these threads a few times. Lincoln's not talking about any constitutional process. He's specifically talking about Texas' right to rebel against Mexico and control as much land as they can and tying it to the natural right of rebellion. The south had every natural right to rebel, just as the north had every natural right to suppress the rebellion. Natural rights are fairly dog-eat-dog. The "social contract" is our surrender of some of those natural rights in order to enjoy the benefits of civilization. Note the clauses in the Constitution that speak of suppressing rebellion. What the south didn't have was a legal or constitutional right to secede.
What I always find interesting in researching this stuff is the extent to which people assumed that a break up of the union would cause civil war. Time and again you find people warning that the sectional differences would lead to war.
Indeed. Yet most people on both sides, having an exaggerated sense of their own military capabilities, assumed it would be a ninety-day war. Only a few, like W.T. Sherman, and Jefferson Davis, knew better.