Before he went along with the 'Court Packing' scheme, F.D.R. mulled an Amendment to the Constitution specifically allowing for a clarification of the Commerce Clause (i.e. allowing Congress to regulate industry). Assuming Roosevelt doesn't threaten to reorganize the Court as IOTL, and the Court as a result does not begin to shift it's rulings, I can see this happening in the long term.
In the short term, however, you'll probably see Roosevelt doing his best to divide his programs (ala Unemployment Insurance) between state and federal control, in order to salvage what he can from the 'Horse and Buggy' Court.
One aspect of this is going to be the severe unpopularity of the SCOTUS itself. That's not going to do well in the 'keeping the respect of the public' on the part of the SCOTUS if said body keeps ruling popular programs unconstitutional. Which means that Roosevelt might be able to enact more drastic reforms of the system itself (a more structured reorganization plan, perhaps?).