The government already owns a 60 foot zone from the Mexican border in all of te states except Texas. They should be able to build a wall and road in large sections of that without an issue. If we need more than 60 feet, then there could be court battles. It almost makes any suits moot because te main objection would be the wall and that should only take about 10 feet.
https://en.wikipedia.org/wiki/Roosevelt_Reservation
A free 8 read more, the Roosevelt Reservation is only on what was Federal and tribal lands. May still have some private lands not covered.
Many times eminent domain, the taking of te property happens fast, it is just the price that ends up in dispute.