WASHINGTON — Congress, at odds with the president, was struggling to assert more control over the federal government through the budget process but could not seem to wrap up its work on deadline. So the House and Senate voted to change the budget-making process, and lawmakers gave themselves a deadline extension to get their fiscal house in order.

That was in 1974, and it worked, sort of. The new law, the Budget and Impoundment Control Act, enacted in July 1974 over the veto of President Richard M. Nixon, gave Congress a “transitional quarter” in the summer of 1976, pushing the deadline back three months. Today, 39 years later, there are no more nightmares about a government shutdown on July 1. Now it happens on Oct. 1. (Nearly all states still begin their fiscal years on July 1.)...