Make them do it. Does Trump want to keep his support and go down fighting or does he just want to get the same old label the rest of the pubbies got. If his support turns on him then everyone will be laughing at him.
There’s no “make them do it” in our government. Remember we went Obie’s entire first term without even debating a budget. Most of the government runs on automatic appropriations and doesn’t an approved budget anymore. The parts they “shutdown” are really just a show, and they don’t have to make it so anybody even notices the government has “shutdown”. So Congress can sit pretty in the knowledge that if Trump doesn’t sign a budget it doesn’t matter. He simply has no power in this, any “fighting” is just for show. If Congress doesn’t want the wall in the budget it simply will not be in the budget, period.