Obviously they did not. Perhaps you meant that they had a legal right to do so, which seems not to be totally without dispute. If they had the power they would have won.
The 10th Amendment speaks of powers remaining with the states or the people. And the statements clarifying what the Constitution meant voted for by Hamilton and Jay in the New York ratification said, "... every power not granted thereby remains with them and at their will ..." It was in that sense that the South had the power. But you knew that.
A speech given in a ratifying convention is a weaker indication of original meaning of a Constitutional provision than debates in the Constitutional Convention, and understanding of the common interpretation of the plain words.