Alex Tabarrok ran some numbers, breaking the stimulus plan down by state. Below is the relation of infrastructure spending per person versus the unemployment rate. The red line is the best fit line for all the data points. Note it's sloping down.
The basic logic of a stimulus package is that government will create jobs, people spend the money, which creates more jobs, which allow people to spend the money again, etc, increasing money's "velocity." But here we see the states with the least unemployment get the most money and with the most unemployment get the least money (with some outliers). I can think of three explanations. Here they are in decreasing likelihood.
Shut up. This relationship is because congress members are using the package to send money to their home district/state. Those with the most political clout/understanding get the most money. This package really isn't about helping the whole economy but about boasting one region at the expense of another in order to get re-elected.
Oops. The government made a mistake. Some numbers got mixed up and checks are being sent to the wrong states. Granted, it's a pretty big mistake and one must wonder how an institution which make such mistakes will rationally plan us out of this mess.
Holier Than Thou. We missed something and the U.S. government knows what's going on but this graph doesn't capture all we need to know. If it did, everything will fit together very logically. This is possible, but no where near as likely as the other two.