The way I see it is this - Trump was elected primarily on the Wall - control of immigration was THE issue that brought out his base (protectionism was what switched the Upper Midwestern states to his column).
He has always meant exactly what he said: he will build a Wall, one way or the other (if Congress doesn't appropriate, he'll use the military to do it), and he will make Mexico pay for it (through taxes on cross-border transfers if nothing else).
He believes in those things, he campaigned on them, he was elected on them, and he's not going to back down. Also, he has the tools at his disposal to get it done through executive powers if Congress won't play along.
Nothing ultimately will stop him other than losing the 2020 election, and his holding fast on the Wall - even if it means keeping the government shut down until the election - will significantly determine whether or not he wins re-election.
Either Congress will cave and the Wall will start going up before 2020, or Congress will hold fast as will Trump, the government shutdown will be the longest in American history, and before the election Trump will have the military start building the wall.