Multiple Pentagon officials have privately said deploying troops to the southwest border will hurt “readiness” — military jargon for having enough forces trained and ready to fight. It also runs contrary to the Pentagon’s renewed emphasis on “lethality,” a military buzzword that refers to the ability to quickly overpower enemies.

“You’ve got 5,000 troops that are trained and ready, and we’re using them for something other than their intended mission,” said Todd Harrison, the director of defense budget analysis with the Center for Strategic and International Studies in Washington, and a close watcher of the Pentagon’s budget.

“And when they get back,” Mr. Harrison said, “they will have not been doing their normal training, and won’t be ready if something happens.”