Thereafter, cabinet departments sent their revenue requests to the bureau, which put together a comprehensive spending plan along with revenue estimates. Because Congress lacked similar bureaucratic machinery, members had no choice but to accept these estimates. They usually could do little more than tinker with the executive branch’s spending requests and add their own.

In 1939 President Franklin D. Roosevelt brought the Bureau of the Budget into the White House to exert tighter presidential control. This proved the high-water mark of presidential budgetary dominance.

In 1946 Congress passed the Legislative Reorganization Act to give lawmakers more say over the budget. It required Congress to decide on a maximum spending level for the fiscal year before considering the 12 departmental appropriations bills. But this proved beyond Congress’s ability. In 1947 the House and Senate couldn’t agree on a spending figure. In 1948 they set a limit but then exceeded it by $6 billion—almost 20% of total outlays. In 1949 the two chambers again couldn’t agree on an amount. After that, the requirement was ignored. Budget discipline in Congress eroded as members faced pressure to bring home the bacon to 535 separate constituencies.

Meanwhile, both the president and Congress already had ceded significant control over parts of the budget. In 1847 Congress authorized the Treasury to pay interest due on the national debt without a specific line item in the budget. In 1935 Congress established Aid to Dependent Children, the first entitlement program, under the Social Security Act. The money these families received also could be paid without a specific appropriation, a model followed by all later entitlement programs. Fast-forward to today, and three-fourths of all federal spending isn’t part of any budget process—the Treasury simply pays it out.

The president remained in charge of drafting the rest of the budget, although Congress kept increasing spending on a piecemeal basis. Lacking a line-item veto, presidents had little choice but to accede to these extra appropriations. To rein in this spending, presidents increasingly turned to “impoundment.” While the Constitution gives Congress the sole power of the purse, that power is negative. “No Money shall be drawn from the Treasury,” says Article I, Section 9, “but in Consequence of Appropriations made by Law.” There is nothing in the Constitution requiring the president to spend appropriated funds—he can instead impound them. Thomas Jefferson was the first president to use this power, in 1803.

In 1966 President Lyndon B. Johnson impounded from the budget $5.3 billion, almost 4% of total spending, in an attempt to fund the Great Society and the Vietnam War while containing inflation. President Richard Nixon, however, went too far: After Congress passed the Federal Water Pollution Act over his veto in 1972, Nixon impounded the $6 billion appropriated for the act. In effect Nixon was negating the veto override, directly challenging Congress’s power to make the laws.

The result, voted in as Nixon’s presidency was collapsing amid the Watergate scandal, was the Budget Control Act of 1974. It is still the most misnamed legislation in American history, for it let Congress control the budget—meaning no one was in charge. Accordingly, the federal budget went reeling out of control.

The Budget Control Act outlawed impounding and established the Congressional Budget Office, which is under the control of Congress and largely duplicates the work done by OMB. But the CBO gave Congress the ability to create its own revenue estimates and cost projections. Ever since, the president’s budget, submitted by law before the first Monday in February, has been routinely declared “dead on arrival.” Instead, the budget is drawn up by Congress. Unless the president vetoes one or more of the 12 annual appropriations bills, he has little say over federal spending.

And the president can’t veto a bill that Congress doesn’t pass. Since 1977 Congress has only four times managed to pass all 12 appropriations bills on time, before Oct. 1. In 16 different years it passed not a single one on time. On those occasions Congress has turned to short-term continuing resolutions to keep the government funded. But 21 times Congress and the president have been unable to agree on a continuing resolution. That’s when unessential parts of the federal government shut down until the impasse is broken.

The result has been fiscal catastrophe. As a substitute for budget discipline, Congress has relied on debt. The U.S. national debt has soared by an inflation-adjusted factor of 8.5. In 1974 the national debt was 34% of gross domestic product. Today it is around 100%. This risks national disaster in a future war or depression. “The sinews of war are infinite money,” Cicero observed. But if the national credit card has been maxed out, where does the money come from?

It wasn’t always this way. Seventy-six of the 179 federal budgets before 1975 ran a surplus. Moreover, almost all the deficits occurred in times of war or depression. Since 1975, however, a mere four budgets have been balanced, and those only with the help of phony accounting.

Congress has proved incapable of producing a responsible budget. The president is better situated to set a budget consistent with the long-term national interest. Elected by the whole country, the president would be much more easily held to account politically for failing to impose fiscal discipline and thus has a powerful interest in doing so. If given the power to set the overall budget and impound excess spending, subject to an override by two-thirds of each house, the president would once again be a real player in the budget game. Also give the president a line-item veto, and he would have a powerful tool with which to gather congressional majorities to his side and get budgets passed.

The media has been calling the current shutdown a crisis. But it’s merely an annoyance. The real crisis is that the misbegotten postwar push to marginalize the president from the budgeting process has destroyed America’s fiscal discipline.

Mr. Gordon is author of “Hamilton’s Blessing: The Extraordinary Life and Times of Our National Debt.”