The 7808 doesn't draw amps; it just wastes a bit more power than a switching regulator like a pth08000. The 7808 is more readily available, but wastes a bit more power and you will need to heat sink it. The pth08000 is more efficient and will not need any heat sinking.
If you can, order a pht08000 sample from TI. It's free, and all you need to buy is a resistor and capacitor to use it. It'll give you better battery life.