This is the same line item veto request that Bush requested in 2006 that Congress wouldn’t pass.
In the 90s Clinton v. City of New York, SCOTUS ruled as unconstitutional the line item veto then passed. The difference in this one is that it goes back to the House to reconsider. Given Scalia’s partial dissent in the case, quite frankly, I am VERY worried that with this change to the Bush requested law, SCOTUS may find this one constitutional (though I absolutely don’t think it is).
In short, do I think SCOTUS will uphold this? Sadly, yes.
I suppose it goes without saying, this would be very very bad.