The Dems DO NOT want the President to leave a PERMANENT barrier in any way, shape or form.....despite the fact that people like Obama, Schumer, Hillary etc all voted for a border wall in 2006.
Actually, I think the Donks want the President to build the wall and try to use it against him in 2020 accusing him of being a divider and not a uniter. They just don’t want to be seen as cooperating with him by giving him money. So if he can get any money out of the House, no matter how little, he can counter by saying the funding, even if the majority of it is not specifically funded by the House, was bi-partisan.