Humans have an average energy budget of $100$ Watts, but the power radiated from the body is $1000$ Watts? On average a human consumes around $2000$ kilocalories per day. This converts to roughly $2000000$ calories / $86400$ seconds or around $100$ joules / second giving roughly $100$ watts. 
But if you use human's body temperature of 310 Kelvin, the Stefan-Boltzmann law 
$$P = e \sigma A T^4$$
says the power radiated by a human with a surface area of $2 \, \text{m}^2$ and emissitivity $1$ is 1000 watts.
What's wrong here?
 A: You are forgetting that you also absorb radiation from the environment. The formula you want is 
$$P_\text{net} = \epsilon A\sigma\left(T_\text{skin}^4 - T_\text{env}^4\right)$$
You can find more info on Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/bodrad.html
A: Short answer: 
You are going wrong in assuming that the calorie intake accounts for all of the radiation of the human body. A human body really emits a power of roughly $1\ \mathrm {kW}$.
Long answer: As you've shown, any black body near room temperature with a surface of $\sim 2 \ \mathrm {m^2}$ emits in the ballpark of $1 \ \mathrm {kW}$. This means any object with that surface area and whose emissivity is near 1, emits such a power at room temperature (so even a dead body!). The extra $100\ \mathrm W$ due to calorie intake a human can make use of is usually mostly used in heating, because body temperature is usually at a higher temperature than room temperature. Nevertheless, if the room temperature is at a higher than 37°C (human body temperature), then this extra 100W due to calorie intake will be used to keep the body temperature near  37°C, for example by sweating. 
In short, the extra calorie intake usually translate in emitting $\sim 1 \ \mathrm {kW}$ + $100 \ \mathrm W$. Thus we see that the calorie intake only accounts for about 10% of the total power radiated. That's what you were missing.
A: What is wrong, is that you are using a formula applicable to an isolated system and applying it to a non-isolated system.  
As it has been pointed out, a black body with the given parameters, radiates about 1,000 watts (as an isolated system).  However, in an environment of the same temperature, it also absorbs 1,000 watts. So, the net radiation, is zero!  Only when the environment is colder than the skin temperature, would the person need to use some of the 100 watts available from the food intake.
