WASHINGTON  In a federal budget filled with mind-boggling statistics, two numbers stand out as particularly stunning, for the way they may change American politics and American power.

The first is the projected deficit in the coming year, nearly 11 percent of the country’s entire economic output. That is not unprecedented: During the Civil War, World War I and World War II, the United States ran soaring deficits, but usually with the expectation that they would come back down once peace was restored and war spending abated.

But the second number, buried deeper in the budget’s projections, is the one that really commands attention: By President Obama’s own optimistic projections, American deficits will not return to what are widely considered sustainable levels over the next 10 years. In fact, in 2019 and 2020  years after Mr. Obama has left the political scene, even if he serves two terms  they start rising again sharply, to more than 5 percent of gross domestic product. His budget draws a picture of a nation that like many American homeowners simply cannot get above water.

For Mr. Obama and his successors, the effect of those projections is clear: Unless miraculous growth, or miraculous political compromises, creates some unforeseen change over the next decade, there is virtually no room for new domestic initiatives for Mr. Obama or his successors. Beyond that lies the possibility that the United States could begin to suffer the same disease that has afflicted Japan over the past decade. As debt grew more rapidly than income, that country’s influence around the world eroded.