The President does not have the power to override state and local policies on social distancing

Robert Chesney, Can the Federal Government Override State Government Rules on Social Distancing to Promote the Economy? Lawfare, March 24, 2020.

Trump can say what he wants, and that will affect those who believe in him and that "will translate into mounting political pressure on GOP officeholders at the state and local levels who might otherwise support these measures." And, as a practical matter, there's a limit to compel compliance to social-distancing measures. But the president does not have the legal authority to "order state and local officials to change their policies." Thus:

Our constitutional order has a federal structure, meaning that (a) federal powers are supreme, yes, but limited in scope and (b) the state governments are independent entities, not mere subordinate layers under and within the federal government (that is, the federal-state relationship is not similar to the way that counties and cities are subordinate layers under the state governments).

What follows from this? The federal government cannot commandeer the machinery of the state governments (or, by extension, of local governments). That is, the federal government cannot coerce the states into taking actions to suit federal policy preference. See, e.g., New York v. United States and Printz v. United States. And so, the federal government cannot compel state and local officials to promulgate different rules on social distancing and the like.

There's more at the link.