It would take things to be very bad in my opinion for Mr. Gates to want to go into government. Frankly he's one of the wealthiest men in the world and this would be a personal sacrifice to try to fix things on behalf of his nation. He doesn't have anything to prove to anyone....which if you look back to the first Presidents, is how we selected our leaders.
I don't think he would, ever. Not that its a matter of liking or disliking the US, just that politics aren't in his wheelhouse. Especially now. I would say that politics is now more than ever the art of compromise - which Gates isn't known for.
But, since we are playing this game, I would submit that Edward Whitacre Jr. would be the right billionare CEO for the job. He is tough, pulled himself through the ranks of the Bell System, Eventually became CEO of Southwestern Bell, Later remade into SBC, and was instrumental in the merger of SBC, AT&T, and BellSouth. After AT&T, he did a couple of other things, the most notable being cutting the fat at GM as CEO, which is soon to return its bailout money to the United States.
He knows business.
He knows money.
He has balls.
And most importantly, he has the ability to make hard decisions.