I'm relatively certain the text to Franklin from Jimmy never occurred if he has been unable to switch to Franklin.
Your save is likely buggered up-- My game simply skipped Meltdown back in October, I didn't notice until after I completed "the big score"-- Luckily I had a save right after the Ballad of Rocco-- so reloaded that and repeated the last 10 missions or so.... I do realize your problem is not the same as this.
I'm surprised you can do anything in the game right now if you can't switch characters.
Above someone mentioned getting the game to reload-- this can sometimes unstick things if that is the problem....
Try saving your game in a NEW slot-- exit the game. Start the game and let your new save auto load. Then Kill yourself with a grenade-- see if this does anything.... I would try doing different activities (golf or tennis-- you don't have to do them, just start them and exit) and going online and back off-- hopefully one of these things will get it to unstick....
About the only other thing I would try if none of the other things work (before starting a new game)-- is to delete all the updates and play off line (so the game doesn't prompt you to update)-- load up your game and see if it works without any updates (you can try the save in a new slot, exit, start game, die trick again).
I do wish you luck--- and please post back if any of the suggestions work (or you get it to work some other way).