The US economy grew by just 0.6 per cent in the last quarter of 2007 and the housing market has plummeted following the subprime mortgage crisis.
In January, the job market shrank for the first time in 53 months and fears of a recession have grown.
Bush admitted the US economy was going through a rough patch but said it could absorb problems such as recession, war and corporate scandals.
"The genius of our system is that it can absorb such shocks and emerge even stronger," he said.
However, Harry Reid, the senate Democratic leader, blamed the Bush administration for being partly responsible for the crisis.
"We will fight for families struggling with rising energy prices and a national housing crisis. And we will fight to reverse President Bush's disastrous budget policies that have hurt the middle class," he said.
Rebate cheques are due to start being sent out to taxpayers in May.
The plan also includes a provision sought by the Democrats which allows some low-income workers, retirees on social security and disabled veterans who do not earn enough money to owe income taxes, to receive a cheque.
Businesses will also get tax breaks for investing in new plants and equipment as part of the plan.
In addition to the stimulus package, the US central bank has cut interest rates to three per cent from 5.25 per cent since mid-September in a bid to address the credit crunch that has rocked global markets.