From the Times story on David Paterson's thought process that Isaac linked to earlier:

Ticket balance is also a consideration. Some of Mr. Paterson’s advisers envision a Republican ticket headed by Rudolph W. Giuliani, the former New York mayor, for governor, with Joanne M. Mahoney, the popular Onondaga County executive, as his running mate. Rounding out the ticket might be John J. Faso, the former assemblyman, for comptroller, and Peter T. King, the Long Island Republican, for Senate.

“That’s a white Catholic ticket,” said one person who has ties to the governor’s political team, and who requested anonymity for fear of losing those ties. “And it’s white Catholics upstate they are going to lose.”

According to the tribal logic of New York politics, Mr. Paterson can expect strong support in New York City, among black voters and from staunch Democrats. Ms. Kennedy, a white Catholic, could help in the battleground suburbs of Buffalo, Rochester and Syracuse. But the Democratic ticket already includes Attorney General Andrew M. Cuomo, who is Catholic and already broadly popular in those places.

I guess it's possible that Caroline would have some appeal among upstate Catholics. But my hunch is that the bona fide swing voters among them are much more likely to think "rich, liberal Manhattanite" when they hear the name Caroline Kennedy than "white Catholic." (Surely the Catholics who regard John and Bobby Kennedy as icons tend to be older and more loyal to the Democratic Party.)

--Noam Scheiber