According to a new NBER working paper from Claudia Sahm, Matt Shapiro, and Joel Slemrod, about 20% of households increased their spending as a result of the 2008 tax rebate stimulus, and 50% used it to pay down debt. Thus they argue that there was only a small direct stimulus per dollar of rebate. However, due to the size and speed of the disbursement, they find that the program did have a significant impact on GDP in 2008:

Overall, the results suggest that the rebate program provided only a modest stimulus per dollar of rebate. Nonetheless,the rebates were so large and so quickly disbursed and the fraction spent was spent so rapidly that they had a non-trivial effect on aggregate spending in the second and third quarters of 2008.  Although the rebates clearly did not stave off the sharp drop in economic activity in 2008, they did affect the timing of its onset by making growth in household spending noticeably stronger in the second quarter and noticeably weaker in the fourth quarter than it would have been absent the rebate.