Both those bills are amnesty horrors—and if either passes the House they will be made worse by the Senate.
So we can only hope Trump is pushing them knowing they don’t have enough votes to pass the House. But I don’t like it when he plays that game, as he did earlier with DACA, of saying, “See, I tried to pass it but Congress, and particularly the Dems, wouldn’t agree to it!”
That seems the more likely because he is supporting both bills—which is kind of nonsensical for the supposed hard bargainer.
I believe Donald anticipates a “Children, children!” moment after Dems and GOP piss on one another in public and fail to budge. The president can’t introduce a bill, but can write one (as anybody can).