You can also try to remove some of your earlier savegames in the file itself. Skip the cut scenes, and as soon as you are able open the game menu and load your saved game.
Instead of selecting Continue or Load from the title screen, select New Game. It is unrelated to the size of the save file, and it does not seem to be caused by a 'corrupt save.' In the absence of a permanent solution, you can load from within the game. This issue also affects the PC version of the game in Steam.
This is easily solved, just clear the cache on your Hard-Drive (Xbox 360) and it should then allow you to load. Sometimes, when trying to Continue or Load the game from the main menu, the game will begin loading, but stay loading 'forever' (slides will still change, and the roulette wheel will still spin, but the game will never actually load - tested up to 25 minutes). Following the instructions in the video and shutting off your autosaves will solve the problem, but it will happen again when the game autosaves even when you turn them off (Leaving Caesar's tent does this for example) but just delete the new autosave before the next loading screen and you'll be fine. This fix works on PC, Xbox One, and Xbox 360.
