Under Undersecretary of Defense for Policy John Rood testified in front of the House Armed Services Committee and he confirmed there are two ways President Trump can build the wall without Congress.
The first way is to declare the border a national emergency. If he should take this path, there is plenty of money in the Pentagon he can use to build the entire wall. There would also be money he can use for other safety measures on the border.
The second way is by using 10 U.S.C. § 284 . That law allows the use of the military to build walls and other barriers to stop drug trafficking, Human trafficking and to keep out organized international criminals.
Here is Mo Brooks questioning Rood:
Mo Brooks: Does 10 U.S.C. § 284 as you understand it, require the declaration of a national emergency before it is implemented?
John Rood: No.
Mo Brooks: It does not?
Brooks: Has President Trump, to your knowledge, ever used 10 U.S.C § 284 to direct the military to build the wall that is necessary for border security?
Rood: No, not to my knowledge, Congressman.
Brooks: If President Trump were to direct the Pentagon and the United States military pursuant to 10 U.S.C § 284 to build such barriers as are necessary to secure our southern border from drug trafficking and international crime cartels would the United States military obey that order?
Rood: If we judge it to be a lawful order, yes sir. And I assume it would be.
The problem with declaring an emergency is that you are giving the next president the power to declare global warming or gun ownership, a national emergency. There is one small problem with using the Department of defense. They can only build in drug trafficking areas or areas where organized criminal use. But, the wall will cause drug traffickers to find another route to distribute their poison and then the DOD could build there too.