Some proposed reductions in federal spending are clearly specified. The budget assumes, for example, that the government can save $48.8 billion in disability payments by returning to work men and women who the government has previously concluded are unable to work.

Other proposed reductions are unspecified, like a “two-penny plan” to reduce discretionary spending by 2 percent a year. That wide-ranging category of spending includes everything except the defense budget, interest payments and obligations like Social Security. But the administration provided no details about the particulars of the plan, just an estimate that the cuts would save $1.4 trillion, or about 40 percent of the total reduction in federal spending.

A combination of fiscal restraint and faster growth could quickly render the federal debt much more manageable. The standard measure of government debt is in comparison to a nation’s economic output. Under Mr. Trump’s budget, the debt would decline from 76.7 percent of annual economic output in 2018 to 59.8 percent of annual economic output in 2027.

By contrast, the Congressional Budget Office estimated in January that under current law the debt would reach about 88.9 percent of annual economic output over the same period.

“The C.B.O. assumes that we’ll never grow at more than 1.9 percent again,” said Mick Mulvaney, director of the Office of Management and Budget. “That assumes a pessimism about America, about the economy, about its people, about its culture that we refuse to accept.”

But economists generally regard the projection of 3 percent annual economic growth as highly optimistic. The Federal Reserve estimated in March that the maximum sustainable pace of economic growth is around 1.8 percent. The Congressional Budget Office puts the ceiling at 1.9 percent. Those are low numbers by historical standards, but growth is determined by the expansion of the work force and the improvement in the amount that workers can produce. The growth of both the working-age population and productivity have slowed in recent years.

“Without violating some of the most basic laws of economics and history, we are not going to get the kind of growth that will yield a balanced budget in 10 years,” said Steve Bell, a former staff director at the Senate Budget Committee who is now at the Bipartisan Policy Center.