Chris Foresman at ArsTechnica shows some references from within iOS for upcoming quad core devices as well as a few arguments for why they're probably coming.
9to5Mac believes that Apple may have designed the A6 to be quad-core all along, and could introduce it to the iPad 3 expected in early spring. The reasoning is that ASUS has already shipped its Transformer Prime convertible Android tablet featuring a quad-core Tegra 3 processor, and Acer and Lenovo have plans to ship Tegra 3 tablets in early 2012, so Apple won't want to appear to be behind the competition. But that doesn't necessarily mean that Apple will immediately follow suit—several dual-core Android smartphones shipped well before the iPhone 4S and Apple still managed to sell record numbers of the single-core iPhone 4 in the interim.
My take: I predict Apple will put out a quad core processor in their next iPad, but they won't do it because of what their competitors are doing. The iPhone 4 with its single core 800MHz CPU was still responsive than nearly every Android phone in existence when they were bearing dual-core 1+GHz behemoths. Apple doesn't bump the specs just for the sake of bumping specs. It bumps product specs according to how it wants its specific devices to perform with specific software. This is the advantage of its integrated in-house hardware and software.
Apple will put a quad core processor into their next iPad if it is necessary to get the device to perform as they want it to. If the "retina" quad-resolution display iPad everyone claims to be coming does come out, there's probably no escaping the necessity of a massively more powerful CPU and GPU.
Caveat to my prediction: If there's no retina display, there's no quad core cpu in the iPad.