This weekend the federal shutdown becomes the longest in history—and yet, and yet, the sky has not fallen. Meet the team that has allowed the Trump White House to hold out for so long, and in the process forever altered future shutdown fights.

Across the street from the Oval Office, an only somewhat merry band of budget lawyers labor on one priority: making this event as painless as possible. That was the order from President Trump when the government closed, and the Office of Management and Budget was ready. Acting White...