Whether President Trump needs Congress to authorize construction of additional fencing at the Southern border is an open question. Given the invasion taking place there, many observers believe that the president, exercising his powers as Commander in Chief, can simply order the Army Corps of Engineers, or another appropriate branch of the military, to proceed with construction. Of course, that construction would have to be paid for. But I assume there is enough money rattling around the executive branch that could be brought to bear on one basis or another.
I think that view is probably correct, and I also think that the present Supreme Court would likely agree with it–although the wall could be finished long before the Court could rule.
Today on Instagram, President Trump told the world that he has reviewed the question, and thinks he has authority to order construction of the border wall. He is giving negotiation with the Democrats “a shot,” but retains the option to leave Nancy Pelosi in the dust and proceed with construction:
I would like to see the president exercise his authority to resume construction of the wall. Illegal immigration is a crisis that desperately needs to be addressed. The Democrats have made their position clear. It will be up to the voters to decide whom to reward and whom to punish.