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A device that can't supply enough current will fall out of regulation and go under voltage rather than over.
What people have posted here is correct, the consuming device will draw the current it requires, a device requiring 3A at 12V will draw 3A from the power supply even if the supply is rated at 50A, it just means that the supply could be connected to more things at once.
There is such a thing as a constant current power supply but they are a sepcialised device and you won't see them normally, I am sure there would be an application for them in the lab but I can't think of it at the moment. They are used in things like car MAF (Mass Airflow) sensors where they apply a fixed current to a wire with a large temperature coefficient (A large resistance change with temperature) The current is fixed so the voltage across the hotwire will change with the amount of air flowing across it (Resistance in ohms multiplied by current in amps giving the voltage, the constant current heating the wire to a known temperature and the airflow cooling it)
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