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"Mandate", in this sense, means that this Congress shall force all states to comply with their healthcare legislation, and that not complying is a federal offense.
Congress is way outside it's authority here; The states have the right, at present, to facilitate health care coverage providers whom operate nationally, and some internationally.
This Congress and administration is forcing its "mandate" onto the states to comply with its wishes or face economic sanctions; In a word, blackmail. This Democrat Congress is using stimulus money to the states, like a drug dealer uses crack on his customers.
If Congress facilitates a "federal healthcare plan" that is optional to the states, in addition to their already existing health care providers, this would be within the federal governments Constitutional guidelines.
But, as anyone can see, this is not what Congress or the administration wants.
This legislation is an expression by Obama, to display his personal prowess in getting his way. And a display by this Democrat controlled Congress to show that they have whatever power they wish to exercise on the states, since they hold the states in debt to the federal government.
This is opposite from the way the Constitution delineates states rights.