He announced that he would call a fiscal summit on Monday to discuss an inherited deficit of $1.3tn.
An unnamed US official was later quoted as saying Mr Obama intended to cut the deficit in half by the end of his first term.
This would be done by scaling back on the war in Iraq, increasing taxes on those earning more than $250,000 a year and making government more efficient, the official said.
Mr Obama said he would address the nation about his priorities on Tuesday before issuing a budget on Thursday.
"I'll release a budget that's sober in its assessments, honest in its accounting, and lays out in detail my strategy for investing in what we need, cutting what we don't, and restoring fiscal discipline," he said.
However, he also warned of the challenges ahead.
"As important as it was that I was able to sign this plan into law, it is only a first step on the road to economic recovery.
"None of this will be easy. The road ahead will be long and full of hazards," he added.
"But I am confident that we, as a people, have the strength and wisdom to carry out this strategy and overcome this crisis."
The stimulus plan, which was approved by Congress just over a week ago, aims to save or create 3.5 million jobs, boost consumer spending and rebuild infrastructure.
Over the past week, Mr Obama has also announced measures to assist families facing foreclosures, and those struggling to meet mortgage payments.
But Republicans, only three of whom voted for the stimulus package in Congress despite calls by Mr Obama for bipartisan support, have said the new tax cuts are insufficient.
They have also complained that the president's spending plans will leave the US economy saddled with debt for years to come.
"We can't borrow and spend our way back to prosperity," Republican Dave Camp said in his party's weekly address.
"If he [Mr Obama] is serious about dealing with the tough issues and getting spending under control, his budget will show it."
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