One division in a nation of 150 million doesn't make for "stabilization" -- even if they're invited.
The US interests are far better served if Musharraf can stay alive and keep it in the road.
I didn't mean stabilize the country. I quotation marks around "stabilizing" because it would not be our real purpose to being there. We would be wise to go in, under the guise of attempting to help China and India stabilize the situation, but with the real intent of conducting stepped-up operations against Al-Qaeda and other terrorist organizations and supporters in western Pakistan, where we suspect Bin Laden of hiding. Ship a rapid deployment force into Afghanistan, get organized, then move into western Pakistan.
"If India could, they'd take over Pakistani Kashmir as well (again, same reason: elections in 2004) and that would only create an even bigger long-term mess."
In the chaos that ensued, I think that Pakistan would be more worried about survival than stopping India from getting Kashmir. It would, in my opinion, be a fine opportunity for India to move in and settle the dispute once and for all - occupy it by force. That, to me, seems an improvement over the current standoff.