We examine the ability of the government to increase consumption by evaluating the impact of the 2009 “Cash for Clunkers” program on short and medium run auto purchases. Our empirical strategy exploits variation across U.S. cities in ex-ante exposure to the program as measured by the number of “clunkers” in the city as of the summer of 2008. We find that the program induced the purchase of an additional 360,000 cars in July and August of 2009. However, almost all of the additional purchases under the program were pulled forward from the very near future; the effect of the program on auto purchases is almost completely reversed by as early as March 2010 — only seven months after the program ended. The effect of the program on auto purchases was significantly more short-lived than previously suggested. We also find no evidence of an effect on employment, house prices, or household default rates in cities with higher exposure to the program.
From here via here.
The Cash For Clunkers program has apparently had some long term impact on the prices of used cars (increasing them), and some environmental benefits (although very expensive to accomplish ones). So it wasn't utterly worthless. But, it was a dud when it comes to increasing spending on automobiles more than very briefly and then at the expense of sales in the near future.
The housing purchase tax credit similarly shifted many home purchases by a few months but does not appear to have changed the total number of housing purchases beyond the very short term much at all.
Basically, the effects look very close to the hypothetical "money drop" that economists talk about as stimulus.