Speaking to reporters this month, Jim Mattis, the departing defense secretary, said the rotating schedule of units and the gradual drawdown of troops on the border are part of why the deployments would not have an “appreciable impact in military readiness.” Mr. Mattis resigned on Thursday, and will leave the Pentagon by Jan. 1, over what he described as a differing approach with Mr. Trump over military worldviews.

Marine Col. Amy R. Ebitz, a fellow with the Brookings Institution, said the border deployment might actually help readiness, not hurt it. She noted that troops who are welding structures and driving around Border Patrol agents are still engaged in training — even on tasks unrelated to combat.

“It’s an opportunity to train,” Colonel Ebitz said. “We do it all over the world, so why would our border be any different?”

As evidenced by the duties at Fort Hood, the border missions also affect the soldiers still in garrison. The deployment has taxed — if not heavily — how the Army trains and prepares to go abroad on a deployment schedule that is planned and orchestrated months in advance.

It also comes after concerns by top Defense Department officials that 17 years of war in Afghanistan and Iraq has made troops battle-hardened and ready to fight terrorists and insurgents, but unprepared for conventional warfare against big state armies.

Pentagon officials worry that Mr. Trump may try to extend the border deployment well into 2019 to show his political base that he is tough on immigration issues. Such a move, Defense Department officials said, would run counter to his administration’s national defense strategy to prepare for conflict with world powers like Russia, China, North Korea and Iran, after almost two decades of fighting terrorism.

On Twitter this month, Mr. Trump suggested that troops would finish building sections of his proposed wall on the southwest border if Congress refused to fund the project.