Leaving aside my doubts about the fairness of the currently proposed stimulus packages, government could still justify executing them if they were effective in helping the economy. Here I will try to rationalize why they won't be, and propose a much more effective and ethical way to spend taxpayer money on economic improvement.
First let's recognize that recessions have both desired and undesired effects on the economy. Recessions happen when the rate at which non-viable businesses die temporarily exceeds the rate at which new business is created. The increase in the destruction rate can be set off by many different reasons, but remember that that rate is never zero even in the best of times, and this destruction is both necessary and healthy. The unhealthy (undesirable) effects are the self-reinforcing negative feedback loops that usually accompany recessions - and these effects are mostly psychological.
Consider this example. Let's suppose people think the country is in a recession. Naturally, they expect job cuts and start worrying about their own security. In a country like USA loss of a job is a pretty severe blow to most families - you lose medical insurance, and unemployment assistance is only available for a short time. Therefore, anyone worried about their job naturally restricts their spending and tries to save as much as possible to protect themselves. If half of the families in US try to cut their spending by just 5%, a lot of the industries that rely on discretionary and semi-discretionary income could see huge drops in revenues, up to 50%. This may happen even if the actual unemployment rate does not increase at all, purely due to the fear. Of course, as revenues fall, this fear of job loss becomes a self-fulfilling prophecy as businesses contract and lay off workers. From here on, this becomes a self-reinforcing feedback loop. And that is the part of a recession that is not justified by the economic fundamentals and is entirely undesirable. Businesses that are viable in normal times suddenly find themselves bankrupt, and so on.
The idea behind stimulus based on creating arbitrary government projects is to pick up the slack in spending that workers who are unemployed (or insecure) have caused, and thus help healthy businesses live through the downturn. This is where things get tricky, however. This spending-for-the-sake-of-spending stimulus idea was not bad in the 1930s, or even 1950s, when most of the income was spent on necessities like food, and not a whole lot of spending could be called fully discretionary. A lot of decrease came from the people who actually become unemployed, and therefore the negative feedback was weaker (since the purely psychological component was much smaller).
Today, the economy looks much different. With 70% of it being in the service sector, the discretionary spending is a very big fraction of total, and it is much easier for people to cut their expenses. This means that the psychological negative feedback is much stronger than that driven by pure financial fundamentals. The stimulus now is supposed to pick up the tab not only for those who are out of funds, but also for those who have money but decided to willingly withdraw from the excessive consumption. Trying to counter that consumer withdrawal with government spending is like pissing against the wind, or shoveling against an avalanche. You achieve little, and risk getting yourself in trouble.
Instead, government should try to directly attack the purely psychological component of the negative feedback loop. How do you do that? By reducing the incentive to save for the rainy day.
People are worried that without the jobs, there would be no medical insurance and no food or housing for their families. Government could just give a blanket guarantee on these things and eliminate most of these worries entirely. It would have a lot more effect on the economy than direct government spending on random projects, like in Obama's plan. It would also cost a lot less.
To understand the scale of the numbers involved, remember that Obama's universal healthcare plan is supposed to cost additional 100$ billion a year. So if we took just the original TARP money we could eliminate all healthcare worries in the country for 4 years. Remember that Fed and the government already given guarantees worth over 10$ trillion dollars to the banking sector. Imagine how much less money would we need if we simply guaranteed food stamps and housing stamps for anyone who gets laid off? I bet that would do a lot more good than just doing something for the sake of spending money.
That would also be a more ethical way to use taxpayer funds, since no money would go to the private sector, and even government itself would get a very small windfall, since most of these social guarantees could be provided by existing agencies like Medicare without major increases in funding.