Is Federal Spending Biased Against Republicans?

No.

But that's not stopping some conservatives from arguing that Obama's stimulus is ruthlessly designed to shower money on Democrats at the expense of Republicans.

Veronique de Rugy recently published a paper in which she claimed that congressional districts who elected Democrats were receiving a significantly disproportionate amount of stimulus money. Nate Silver embarrasses this argument by pointing out that if you bother the check the cities in the most "stimulated" congressional districts, 18 of the top 18 recipients were state capitals, listing in relative order of state size. This isn't exactly black art. Stimulus money goes through state agencies. These agencies are housed in or near state capitals. These state capitals tend to vote Democratic.

In fact, the argument that Republicans are footing the bill for lavish spending on Democratic states might be backward. Harvard's Jeff Frankels finds that the relationship between federal spending and conservatism in the states actually flows in the opposite direction: conservative states get more government largess per buck.

He plots the relationship between federal expenditures per dollar of taxes paid on the X-axis (2005 data) against percent of Republican votes per state on the Y-axis. In other words, as you move to the right along the X-axis, states receive more federal spending per tax dollar. As you move north on the Y-axis, states get more Republican. Here's the graph:
Per usual, Ryan Avent at the Economist strikes the perfect note: It's tempting to make this a huge gotcha! and slam the Tea Partiers for cognitive dissonance, but it's more useful to use this graph as a basic civics lesson. Big rich states tend to pay more taxes (and lean Democratic), while poor, rural (Republican-leaning) states contribute less but receive disproportionate federal spending -- perhaps this goes back to their two senators giving them higher per capita representation in Washington. That's not a political point, it's just the way things are. Economic analysis would be more clear-eyed if researchers took off the red/blue shades.