My Xbox 360's power supply cord is very loosely connected. I've tried to push it with force, didn't go further. Games lag a bit (GTA IV, for example) at graphically expensive situations. Simplier games like Limbo and Worms run without any problems. I think my console suffers from voltage drop because cable isn't properly connected.Power cord looked like this already when I connected my console for the first time. Now my Xbox 360 S is only couple of days old. Please tell me what your consoles look like. Power supply's light is also orange. Not yellow, not red - orange.
It's not possible to drop voltage as you said. It's either connected, or it's not. The power won't wain. It just won't work at all if not properly inserted. But if the power cord won't seat properly in a brand new console, you're still under warranty. I'd get it replaced if I were you..
