According to Ryan Lizza in an October 2009 New Yorker article, Obama's economic advisors, led by Christina Romer, recommended a much larger stimulus package, at least $1.2 trillion dollars, to help fill what was then predicted to be a $2 trillion hole in the nation's GDP.
Conservative political calculations prompted Congress to scale back the Recovery Act to its enacted form, which was meant to keep the economy from collapsing altogether, not from bringing it out of a recession. Despite the shortcomings, the Recovery Act has created millions of jobs, stimulated the economy, and boosted the national GDP — without it, the U.S. might have been worse off.
Still, a second stimulus package could jump-start the Recovery Act to finally lower national unemployment rates, says OMB Watch:
The second stimulus should not follow the blueprint of the first Recovery Act. About one-third of the Recovery Act was comprised of tax cuts, which, while helpful from a political standpoint, do not help the economy nearly as much as other forms of spending, at least in terms of having a multiplier effect. Of course, that's not to say that Congress should completely ignore the original stimulus' architecture: the act's prioritization of infrastructure projects, of reinvesting in the nation, was a good one, and should be repeated in the second stimulus.