Wasn;t it determined that no one actually spent that money and just paid of debt instead?
https://www.nber.org/papers/w15421
"Only about one-fifth of respondents in the Reuters/University of Michigan survey report that the 2008 tax rebates led them to mostly increase spending, while over half said it would lead them to mostly pay off debt... [T]he results imply that the rebates provided only a modest stimulus to spending per dollar of rebate."