As everyone knows, if you are an undocumented immigrant the simplest solution is to claim to be a US citizen. Life becomes really easy after that, especially after you buy fraudulent documents like birth certificate and Social Security card, often assuming the identity of another American. The only thing is that it is a serious crime, and unless you have a compelling story to share with an immigration judge, there is no way to become legal. It seems, though, that with an overworked USCIS, a no-enforcement of immigration law environment, and many naturalized citizens who now work for DHS/USCIS, it is apparently easy to get away with anything.
Take a look at the story of an illegal alien below who worked without authorization claiming to be an American citizen and got away with it by lying under oath. Not that you should too, but it seems that people are getting away with it for the time being. The huge risk is that if you are caught, then you are doomed.