Lincoln's talking about the Right of Rebellion, a natural right, not a Constitutional right. The idea goes back at least to Locke, if not further. And when Lincoln says "Any people any where" he could just as easily be talking about slaves in the south. Would you argue that they had a Constitutional right to revolt? Did the Whiskey Rebels? Note that the Constitution talks about suppressing insurrections. How could the government do that if, constitutionally, everyone has a right to "rise up and shake off the existing government"?
Note also the phrase "having the power." The south didn't. Bad luck, that.
How the hell did you come up with that? Did you not read the quote?