Well, let's say a state did that. And it went to the Supreme Court. What would they have said?
Well, there was this rather famous 1833 case (right around the same time, huh?) of Barron v. City of Baltimore, 32 U.S. 243 in which Chief Justice Marshall (one of the Founding Fathers, by the way) gave the opinion.
"The constitution was ordained and established by the people of the United States for themselves, for their own government, and not for the government of the individual states. Each state established a constitution for itself, and in that constitution, provided such limitations and restrictions on the powers of its particular government, as its judgment dictated."
"Had congress engaged in the extraordinary occupation of improving the constitutions of the several states, by affording the people additional protection from the exercise of power by their own governments, in matters which concerned themselves alone, they would have declared this purpose in plain and intelligible language."
"In almost every convention by which the constitution was adopted, amendments to guard against the abuse of power were recommended. These amendments demanded security against the apprehended encroachments of the general government-not against those of the local governments. In compliance with a sentiment thus generally expressed, to quiet fears thus extensively entertained, amendments were proposed by the required majority in congress, and adopted by the states. These amendments contain no expression indicating an intention to apply them to the state governments. This court cannot so apply them."