By Kevin Connolly
BBC News, Washington
The president said defence and health would be exempt from the cuts
Keeping the national accounts of the United States is one of the biggest and most important jobs in world governance.
It is also the dullest, because it involves painstakingly collecting information about billions of transactions - and constantly revising estimates in the light of changing circumstances.
It is big because of the sheer size of the American economy. The national debt currently stands at more than $12tn - if you took that amount of money in $10 bills and laid them end-to-end, it would reach the sun, more than 90 million miles away. Actually that statistic is slightly out of date - it would now reach quite a bit further into space.
And it is important because for all you read about the rise of China and the emergence of India and Brazil, what happens in America matters enormously to the rest of us, as American consumer demand remains a powerful locomotive for pulling the wider world out of recession.
So there is good reason to look hard at the $3.8tn budget President Obama has proposed, at the numbers that underpin it and the assumption on which it rests.
In political terms, Mr Obama came on like a deficit hawk, sternly warning Washington that the time had come for politicians to "stop acting like they were spending monopoly money".
He did not mention his predecessor by name, but there were harsh words for George W Bush, who was castigated for funding two wars and several tax cuts through borrowing rather than cutting spending elsewhere.
It is a smart move for Mr Obama to sound dry and disapproving of profligate government.
His Democratic Party has lost three important elections in recent months (a Senate seat in Massachusetts and the governorships of New Jersey and Virginia).
Those defeats were worrying signs for the White House that the kind of independent centrist voters who helped sweep Mr Obama to power might be starting to panic at the costs of the stimulus programme and healthcare reform.
But Mr Obama is by instinct an interventionist, the kind of politician who believes that government works, and he came to office during a recession.
He argues that without swift and aggressive increases in public spending, a bad recession could have become a great depression.
So while Mr Obama wants to position himself as a hawk in the longer term, in the short-term he is presiding over some startling deficits.
In this financial year, the government will borrow more than $1.5tn and next year the figure will be only slightly lower.
The president is trying to win bipartisan support for his budget
Both of those figures are higher than anything reached under Mr Bush. And in the years to come, the White House figures show America continuing to run a huge budget deficit, albeit at something like half the current levels.
But do not forget that the annual deficit is the rate by which the overall national debt is going up every year, so cutting the deficit means slowing down the rate at which the problem is growing, not solving it.
And there are longer term difficulties to remember as well.
First, Mr Obama's stated goal of getting the deficit down to just over $700bn by 2014 is based on a steady growth rate of 4% - that would be quite an achievement, even for the United States.
And on top of that, sometime towards the end of the decade, there will be a spike in retirement as the baby-boomers stop working and start claiming government-funded medical benefits.
The generation that built American prosperity is not going to vote for an administration that threatens their right to a comfortable retirement.
To some extent, Mr Obama's hands are tied.
He talks - as politicians all over the world are prone to do - of eliminating wasteful government spending. But the amounts that will yield are a drop in the bucket set against a deficit that may be heading towards the $20tn mark in a few years' time.
On top of that - anxious to appease his supporters and to avoid giving ammunition to his critics - he is promising to protect certain areas of spending, including defence budgets and spending on health and social security.
That means any savings to come must come from the so-called discretionary areas of the budget which account for only about a fifth of the overall total.
That constraint produced one of the biggest headlines of budget day, with the announcement that the space agency Nasa will not be given the cash to buy a taxpayer-funded successor to the space shuttle for putting astronauts into orbit.
There will be cash, but only enough to commission a vehicle from the private sector.
It makes good fiscal sense at the moment but brace yourself for some angry headlines if America appears to fall behind China, or indeed India, in the race back to the moon and beyond.
In the longer term, Mr Obama plans some sort of commissions which would include both Democrats and Republicans to mull over public spending decisions.
It would be a neat trick if he could pull it off - giving the opposition a share of the blame for unpopular spending cuts would make excellent strategic sense. But of course, he has to persuade Republicans to sign up to it too.
And that of course, brings us to one strong argument that works in Mr Obama's favour.
Republicans who are so concerned about out-of-control spending now did not seem so worried (with one or two honourable exceptions) when it was Mr Bush steering the economy into the red.
Nor are they offering a clear, coherent alternative strategy to set against President Obama's ideas - or at least not one that is getting any traction with the media or the American public.
So the budget gives us a sort of preview of how America's political debate is going to shape up in the coming months.
Against a backdrop of a rising deficit, Mr Obama will attempt to bring spending under control. Expect to hear the phrase "bending the curve downward" quite a bit.
The stakes could scarcely be higher - the long-term vitality of America's economy is at stake.
But unless he can persuade Americans that he cares about debt and knows how to shrink it, Mr Obama's future electoral prospects could be on the line too.