Although I have been reloading since 1975, I was not involved in the hobby during the last primer shortage in 2008, so I did some research.
Apparently, the shortage lasted the best part of one year. Do some Google searches using key words, "2008 primer shortage" for more background on the last situation.
This time there is more manufacturing capacity, but that is more than offset by more gun owners, more guns, and the real threat that Internet ammo sales and other bad gun bills have been introduced into Congress and have a real posibility of passage.
The republicans are NOT your friends in Congress. They stabbed us in the back on January 1, 2013 - bringing the fiscal cliff bill to the House floor WITHOUT a majority of GOP support and, unfortunately, this is likely to continue.
The gun-grabbers in Congress will immediately pick the easiest fruit. That would likely include a total ban on Internet sales of commercial ammo, gun powder, primers, bullets, and brass. Other low-hanging fruit would include a law to create a national registry for all guns and gun owners.