The basic idea is John Kerry as Sec State; that forces a special election, which Scott Brown is all but assured of winning. That changes the balance slightly in the Senate, but more importantly preserves a viable means of building a strong Republican presence in the Senate. Let's face it: most of the Republican Senators either can't become the Old Guard (because they're too fractious, and can be thrown out of office because of that, or never become senior diplomats because of that habit, or they're people you'd never describe as a "mental giant".) More immediately, it gets Scott Brown back in the Senate, where he's popular and effective.
With Susan Collins (R-Maine) doing the cowardly thing and turning on Susan Rice - that happened this morning - the nomination of Dr Rice to Sec State is all but dead. She'd like to see John Kerry in that job simply because she's lost the ability to think beyond what her handlers tell her to think.
The biggest problem with all of this is that they might actually achieve what they want. Which opens a door for Dr Rice to move into another substantive role: National Security Advisor. The other side is that John McCain gets to shout about how he bested the President - a significant talking point for his future prospects as a dead weight upon Senate Republicans.
The only problem with all of this is that Dr Rice could be offered the head of the CIA. Or Defense. When you're playing bare-knuckle politics as Senator McCain is, you can never be sure if your opponent is faking it or you're really doing a number on him. I can guarantee that President Obama is planning both how to handle this whole thing and how to exact revenge. The man is, when you get down to it, quite cold and capable of astonishing ruthlessness. Especially once he's had his nose bloodied, which happened in his first term and in that Denver Debate.
John Kerry might be an effective Sec State (I kind of doubt it, actually), but he's now probably dropped to the bottom of any list - especially as that silly trio have made it clear the man would sail through confirmation hearings. The President has the fiscal cliff to negotiate, fill the various opening cabinet posts and get his legacy started. John McCain wants to stop two of those, the Republicans in general want to stop all three. I don't think they've thought this all the way through. Right now, if I were John McCain, I'd be worried that my plan would work.
Tony Sidaway, on Google+, has the another, probably more accurate, explanation:
It's an interesting idea, but I don't understand why McCain, Ayotte and Graham would risk their reputations just to squeak out a possible Senate seat. It just doesn't make any sense. I'm inclined to the view that McCain cannot think straight when it comes to Obama, and the other three are along for the ride. Sad as it sounds, I think it's basically just "Old man shouts at cloud", no more and no less.