doubt it very much,sometimes they'll allow it but you'll be charged an over the limit fee as well,try not too do it,your only digging a deeper hole for yourself
It is literally only for a couple of weeks though. I'm moving and need stuff for the new house. Then as soon as I get the deposit from my old place back I'll clear the amount that's overdrawn
There isn't actually anything you can't live without for a couple of weeks. If you have a roof over your head and a cushion and a blanket to use at night while sleeping you can manage - getting into debt to buy a fridge or whatever isn't a good idea. Depending on what it is you do need - have you tried jumbletown and freecycle and all those places already?
If you really must, try contacting them to increase your limit - if you have no late payments and are clearing at least the minimum every month, they might consider a small increase. I wouldn't normally recommend increasing credit card limits but it's probably better than the charges and bad reputation that unauthorised credit could lead to .