This was something passed by a Democratic administration. Therefore Republicans hate it, and since 2/3 of the Supreme Court is Republican, it's likely to be struck down.
The actual reasoning comes later. Something-something-Federalist-Papers-something. I'm sure they'll have no trouble digging up some Founding Father who said something that sounds like banning this, if you squint right.
I know a great many lawyers, of both parties, who have more respect for the Supreme Court than I do. They are more informed and better educated than I am, so you should take my cynicism with a grain of salt. But in my experience, treating the Supreme Court as a partisanship machine yields extremely accurate predictions.
When this country was founded, a lot of its residents were slaves, so I'm sure Thomas and Alito will find plenty of fodder in that for their "originalist" stance denying workers rights.
This supreme court has been very down on federal powers, so it really would not be surprising if they pulled "the major questions doctrine" to ultimately kill this off.
That's my take as well. There is almost certainly no doubt that the commerce clause (under current precedents since the 30s) gives Congress the authority to make legal rules like this one. If there be doubt here then it will be about a) the ability of Congress to delegate this power with b) such a vague and all-encompassing term as "unfair" to describe the practices that the FTC may regulate, and/or c) whether this particular rule violates the "major questions" doctrine found in the recent W. Virginia vs. EPA case.