This is not a factional affair. Kevin Rudd and his chosen deputy, Julia Gillard, are from the right and left factions respectively, as are Kim and his sidekick, Jennie Macklin. (Looks sort of like those TV news shows which have paired newsreaders of the opposite sex, doesn't it?)
Frankly, Kim is my kind of guy. He was a Rhodes Scholar who wrote his MA thesis on "Post-Evatt Labor Attitudes to the United States Alliance". He was Defence Minister and Finance Minister under the Hawke and Keating governments. (His dad was Education Minster in the Whitlam government.)
Kevin Rudd is a great spokesperson. He's always on top of his game, he's always read all the reports, he's always there with what-ought-to-be-done. He really knows his stuff when it comes to his Foreign Affairs shadow portfolio (but then he was a diplomat who worked in the embassies in Stockholm and Beijing - he speaks Mandarin fluently). He's from Queensland, where Labor holds just six of 29 Federal seats. Rudd is a devout Christian, but hates American-style religious politics.
Pairing him with Gillard (who, like Macklin, is from Victoria) calms fears from that quarter. She's done some good work fighting Tony Abbott over Health issues.
The folks backing Rudd include Simon Crean, Peter Garrett, Kate Lundy, Harry Quick and (of course) Julia Gillard, of whom I have a high regard.
The main issue seems to be, "just what do we need to do to get rid of this government?"