Depends on the fund that your retirement is funded by . Big corporations can tank, but the state funded pension systems will still thrive on tax generated money .
BIG state revenues HOPE the derivitives markets make them money. Why then, do your taxes keep going up? They're all losing their BUTT! That's why your taxes are going up! Get ready, folks!
I would agree that in general Public pensions are more secure than private ones, but they are not immune. At any level beneath the State your taking your chances. For instance the LA Unifed School District has huge underfunded pension liability and no obvious way to pay for them. The city of San Diego is likely to go bankrupt, and in the process will discharge some of it's pension liability.
It seems unlikely that a State would go bankrupt, but it has been discussed in Oregon where the huge bloated state run pension system is THE driving factor. Taxes are at the limit, and there are structural laws that prevent easy new taxes from being created. It's unlikely but not impossible that Oregon will go bankrupt, and if they do so the explicit purpose will be to discharge pensions. (Voter initatives designed to address the absurd PERS system were thrown out by the Supreme Court, the justices are of course all PERS recipiants, but I'm sure this had nothing to do with it.)
Federal pensions from organizations like the US Army and Post Office are as good as it gets. One assumes the only default likely here is due to inflation. But the amounts will be paid, or if not only canned tuna fish, ammo and gold will have any value and we'll all have a lot bigger problems to deal with .