It's probably not raw memory resources that's the problem, it's probably the way the engine is coded. Any modern gaming PC could probably handle 4-16 player games for Saint's Row. We've got way more memory than a 360 or a PS3, generally. But from what the devs have been saying on the issue, it's likely an issue with the way that they have to control what's loaded into memory in the engine. They have to pull some tricks to get the games to run smoothly on the consoles without being memory hogs, I keep hearing about all this mempool stuff and how they stream assets into memory as needed rather than load them and keep them there for the duration of the game.
So look at it like this, you're on a console and you're playing regular 2 player co-op. You can fly around the entire city, untethered from your co-op partner, but the whole time that it's going on the system has to keep assets in memory for each player's character model, whatever they're wearing, whatever weapons they are using, the cars spawning around them, the area of the city they're in, the peds, etc. Of course each console is doing its own workload, but the more people you have in the game, the more potential for memory overload. What if you had four players, each different genders, wearing different outfits, all hanging out with special vehicles that don't normally spawn in the streets (Bloody Cannoness, Genki Manapult, what have you)? You'd end up overloading the memory pool for the consoles in mere moments. I mean, a PS3 has what, 256 MB of RAM? 256 MB of VRAM, so that's 512 MB total. Most modern PC operating systems wouldn't even load with that sort of memory =P The 360 has a similar amount of memory except that it's system memory which is just shared between regular stuff and graphics processing. In either case, it's more taxing than you'd think when you remember that when devs make games nowadays, they have to accommodate the lowest common denominator, which is consoles (As an aside, I'm not PC master race, grew up as a console gamer but it's a fact that consoles have less power than a PC, no matter what sort of fancy optimization tricks devs can pull to get great stuff running on them)