So is the current problem is because the president can veto congresses appropriations? In a functioning government this seems sensible so the executive has a symmetric check on congress, but currently it gives the president unwarranted leverage.
Congress can override a Presidential veto, but it requires a 2/3 majority, which neither party has by itself (due to parliamentary rules, it's slightly more complicated than that in ways that I don't totally understand, but that's the high-school-civics-version). The President isn't actually necessary to reopen the government: Congressional Democrats and Republicans could come to a deal that got them to the 2/3 mark if they wanted to, even over the President's objections. Whether or not that will happen in this cases is anyone's guess.
