I remember the spin at the time. You are correct.
I do think I remember Justice giving it a hesitant thumbs up, though, after it got tinkered with a bit in the conference committee.
It could be that the Pres might have thought that IF if were unconstitutional that Scotus would kill it.
But doesn't that imply that he was violating his oath? To uphold and protect the consitution.....and signing something that he believes isn't means he didn't do that.