I'm speculating, but I suspect the run on guns is a fear that somehow all this will result in an inability to buy guns, either due to new regulation or a break down of the system. There has already been a lot of stress on the system by which instant background checks (NICS) are backed up, and was actually broken for a short period of time. Which caused short term panic in the gun community that no one would be able to buy a new gun.
The run on ammunition hearkens back to the shortages of especially .22 ammunition in short supply for a few years after Obama was first elected... bricks (500 rounds) of .22 lr was difficult to find in stock, and was costing $70 to $100. Before the shortage, you could buy a brick for as low as $10. That lasted 2-3 years, best I remember.
Aries
~Sign of the Rams