I can't see how wall this standoff ends. The Dems in the house have their constituents totally behind them denying the wall and Trump will lose his base if he backs down. Trump may own the shutdown, but those 800,000 employees own the consequences. I don't know when the pressure changes, but at some point the politicians will feel the pressure shift. Many of Trump supporters and Democrat supporters will begin to feel the pinch. Regardless of who owns the shutdown, it will need to end eventually.
It ends when the pressure of the loss felt by a government shutdown hits the fan. I don't think it's going to be much longer. It will probably entail some sort of face saving measure to attenuate Trump's embarrassment for Trump because he got nothing out of a tragic waste of government providing the services the public needs such as Welfare funding, food stamps, or whatever they call it these days, and income tax refunds. I think they're going to have to say they will revisit the issue at some later date.
