The problem with small "cheap" (typical $200 - $300) cameras is that they are cheap because they don't have a very sensitive photo detectors. They'll be desiged for outdoor lighting. When you come indoors, there just won't be enough light without a flash. But when you're trying to power a camera with the equivilent of a pair of AA battries, you just can't build a flash that's going to be bright enough to equate to outdoor lights for a distance of more than about 10+' away. It takes a pretty powerful flash for these kinds of cameras to even begin to think about something 20' away. Actually, even more expensive cameras won't do very go with more powerful flashes at distances of 20'. I've even got a more advanced (but older) digital camera with an exernal flash, and even that is only really rated at about 16' (though in careful situations, I can manage 25' if I'm not going for a really sharp picture).
So the problem is that to copensate for the low sensitivity of the photo detector, it has to expose it to the reduced light for a longer period of time. And of course during that longer period of time, any slight movement of the camera makes the pictures blurry.