They would. But, in the range of household items, nothing you plug into the wall is going to drop the voltage entering your house. Even your finger. And since voltage is equal to resistance times current, when resistance goes to zero (by inserting tweezers, et cetera, into the outlet) current quickly goes to infinity. We know it's not infinite, but for all intents and household purposes it is boundless.
There are limits on the amount of current wires can carry, but that limit is only significant with the size of wires used inside a house, not so much on the outside.