Well, we don't know their cap situation for this year, but if they trade Rivers, my understanding is they take a big hit. They could also load up on draft picks for next year, which might be wise as this is not exactly shaping up to be a world-beater draft, anyway. It doesn't seem to me that they'll be hurting as much as you think, though they do have some funny money situations to deal with.
Either way, they have the QB they believe in. I think a franchise-trade of Brees might not be such a bad idea. Remember they were thinking about dumping him last year, for a third, maybe a second-rounder. Now they are sitting on a pot of gold in comparison.