I am running Android 2.2 on my Droid, I'm not sure if this is the case for 2.1 but,
Once you start up the camera, hit the menu button (the four lines at the bottom of the phone). When you do this, there are options that appear. The bottom one is recording quality, the one right above allows the flash to be turned on or off (it stays on, it's not just a flash).
If that is not the case with 2.1, and that is what you are using, you can do the following.
Download an LED Flashlight app from the market (there are a few and most are free). Turn on the flashlight before bringing up the camera app. It should stay on while you use the video camera...