This is where Trump's persona comes into play: people expect Trump to be an a$$hole. That's why he's gotten away with so much foul shyt he's said and done. This would have destroyed any other politician, but Trump is unique in this aspect. Him holding the government hostage won't hurt him that much in the grand scheme of things; Dems not being the grownups in this situation will.
Open the government and then we'll discuss the wall.
Pretty simple message to stay on code about. I don't see how Dems don't look like adults with this stance. The wall and a working government have nothing to do with each other. Also its incentive to use the same tactic again. Also as already stated, his offer isn't legally binding and given the behavior of Trump, I wouldn't trust him as far as I can throw him.
As the government remains shutdown, the economy and functions of the government will start to suffer more. It will be Trump who bears the consequences of that, not house Democrats. According to the latest polls, only 29% of the population blame Democrats for the shutdown while Trump along with the GOP are mostly to blame.
You position the narrative as Democrats as being at a disadvantage. Its Trump who will continue to suffer from this.