What deal are you talking about? We already negotiated a new NAFTA. If Trump blows that up then even his supporters will feel like he wasted their time. How do you think Trump is going to look when he says "We never should have signed NAFTA 2.0 because I forgot to account for illegals!"?
(And why would Mexico even want to re-negotiate NAFTA when they know that whatever Trump signs will be a worthless document that Trump could ignore anytime he felt like pulling another stunt? Mexico would be better off waiting until after the 2020 election.)
Democrats in Congress have no incentive to negotiate. Trump proved that with the shutdown stunt.