He stressed that immediate action was necessary, and urged both Congress and Americans in general to support his plan, which he said would mean America would not face a repeat crisis in 10 or 20 years.
But Mr Obama said more time was needed to allow his economic recovery plan to work.
"We have made the tough choices necessary to cut our deficit in half by the end of my first term - even under the most pessimistic estimates," he said.
"We're going to stay with it as long as I'm in this office... Four years from now, I think, hopefully, people will judge that body of work and say: 'This is a big ocean liner. It's not a speedboat. It doesn't turn around immediately. But we're in a better place because of the decisions that we made'."
Referring to next week's G20 summit of the world's richest nations in London, Mr Obama appealed for all countries to bear the burden of stimulating the world economy.
President Obama deals with questions on AIG bonuses
He said it would be unfair to expect those countries taking extraordinary measures to lift up those that were not.
In a letter published in newspapers around the world, Mr Obama called on G20 leaders to "take bold, comprehensive and co-ordinated action that not only jump-starts recovery but also launches a new era of economic engagement".
The meeting will be Mr Obama's first big appearance on the international stage.
Mr Obama said his economic strategy and new budget were based on creating new jobs, rejuvenating the housing market, and creating new liquidity and lending by the banks.
It also features measures to increase health care coverage, higher education spending and a new "cap-and-trade" system on greenhouse gas emissions.
"And we are beginning to see signs of progress," he said.
G20 LONDON SUMMIT
World leaders will meet in London next week to discuss measures to tackle the downturn. See
our in-depth guide
to the G20 summit.
The G20 countries are Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, South Korea, Turkey, the United Kingdom, the US and the EU.
However, the stage is set at Congress for a tough fight, correspondents say.
On Wednesday, Mr Obama is due to meet Senate Democrats in a bid to rally support for an increased deficit, reckoned to be $1.4tn for next year.
The House budget committee will begin writing its version of the budget plan the same day, and on Thursday the Senate budget committee will begin crafting its budget plan for 2010 and the four subsequent years.
Republicans complain that the draft budget expands government and raises taxes on the rich and some small businesses.
"There is little or no Republican support for this budget," Senate Republican leader Mitch McConnell told Reuters news agency.
A Congressional budget office analysis released last Friday estimates that President Obama's budget would generate deficits totalling $9.3tn over the next decade.
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