In order for current to flow (from say 12V to 0V) it needs to lose all of its energy (voltage). Resistance is what causes it to lose its energy, so if there was no resistance would there be any way for it to lose its energy and flow through the wire?
If you consider the case of an ideal wire connecting the two terminals of an ideal (12 V) voltage source, what you have is a logical contradiction. On the one hand, you are saying the potential difference between the terminals is 12 V because of the ideal voltage source. On the other hand you are saying the potential difference is 0 because of the ideal wire.
What this really means is that your model is incomplete. For one thing, all real wires (leaving aside superconductors) have nonzero resistance. For another, all real voltage sources have some internal resistance.
In order to determine what happens when you connect a wire across the terminals of a voltage source, you should consider both these effects. You'll find that the voltage output of the source drops because of the internal resistance, and a large current flows because of the low resistance of the wire. In the real world, likely either the source or the wire will be damaged due to overheating.