The Left controls the media. Any collaboration with the Dems on this, and when it collapses it will be ultimately as spun as the "Republicans' fault." Hell, they're already claiming this thing is falling apart because NO Republicans supported it to begin with, and you want to give them a leg up. Please.
Number #1 rule war: When your enemy is destroying himself, you don't jump in.
What I suggested will ensure the enemy destroys itself.