The new White House budget proposal is built on a deep-rooted conservative belief: The government should help those who are willing to work, and cull from benefit rolls those who aren’t.

That emphasis on work underlies deep cuts and proposed changes to food stamps, cash assistance and health benefits for the poor in a budget that boosts spending for the military and border security. Expect the poor to work in exchange for aid, the White House argues, and antipoverty programs will work better while costing the government less.

If that strategy sounds as if it lacks compassion, says the budget director, Mick Mulvaney, the Trump administration is trying to balance compassion for taxpayers, too.

“We need people to go to work,” Mr. Mulvaney said this week. “If you’re on food stamps, and you’re able-bodied, we need you to go to work. If you’re on disability insurance and you’re not supposed to be — if you’re not truly disabled, we need you to go back to work. We need everybody pulling in the same direction.”