Ah yes, the Commerce Clause. The clause that gives the Federal Government the right to regulate basically anything as long as they can show some tangential connection to "interstate commerce." The Commerce Clause has been found to be pretty damn broad, but not totally unlimited.
You have inadvertently touched on one of the major topics in 1L Constitutional Law!
When it comes to Covid-19, we are in uncharted waters to an extent: Quarantines on this scale have never been seen before. I'm not aware of any rulings on point.
However, logically, the ability to impose quarantines is a decision left to state and local government under the police power. It's a health and safety measure, not a commerce measure. It does necessarily impact commerce, but it's primarily about ensuring hospitals aren't overwhelmed and citizens don't die.
Trump implicitly acknowledged this himself by not imposing quarantines in the first place. Now he wants to lift quarantines he never imposed in the first place. You don't have to be a constitutional expert to realize that makes no sense.
Even Timber admitted states/local governments were in charge of quarantines in some other thread a few days ago. I wonder what he thinks now that Trump has gone and contradicted him
Oh yeah: And MiniAppleIs is right that the Commerce Power, to the extent it exists at all in this case, would have to be exercised by Congress not the President.