What were the implications? Presumably it depends on the ... er, severity? of the violation, but what would the feds do? What have they done historically?
Alabama's governor, George Wallace, attempted to prevent the desegregation of the University of Alabama, which was required by the Brown v Board ruling. He did so by physically blocking the door to the registrar's office. The deputy attorney general was on site and called JFK, who federalized the Alabama National Guard and ordered the commander on the scene to tell Wallace to get out of the way and go into the dustbin of history where he belongs.
He complied.
Somewhat unrelated, but the 'feds' themselves have outright refused to comply with a Supreme Court decision. This was when Andrew Jackson was formulating his Indian Removal Act, which would very swiftly become the Trail of Tears. The issue was that the native groups living inside U.S. borders were technically sovereign nations, so Jackson had no right to force them out. Natives living in Georgia sued the Georgian government over this; the case went to the Supreme Court, led by one John Marshall, which ruled in favor of the natives.
Andrew Jackson's response was, verbatim, as follows:
"John Marshall has made his decision; now let him enforce it!"
As might be implied, the Trail of Tears happened soon afterward.