nothing will go wrong if you don't have enough power. you can start seeing random artifacts and stuff on your screen.........i think, well that's what my friend said.
But also, the psu will probably run hotter if you run like something that is for 400 watt on 300 watt.
You're prone to more frequent crashes and reboots when running a lot of stuff like games.
Also, if the electricity in your house is not stable (like when you turn on that 46 in plasma and the lights slightly flicker) it could cause instability in your computer with weak psu.