I didn’t even realize that cotton was a verb. From The American Heritage Dictionary:
To come to understand. Often used with to or onto: “The German bosses . . . never cottoned to such changes” (N.R. Kleinfield).
The context in which I came across this is a joke, since it is the title of an article about an experiment involving political T-shirts:
T-Shirt Diversity? Bush Won’t Cotton to It.• The question: Which presidential campaign better tolerates dissent?
The experiment: A college professor wears a Kerry-Edwards shirt to a rally for President Bush, then a Bush for President shirt to a John Kerry rally.
Result: Bush people make the subject remove his shirt, then give him the boot. The Kerry people don’t make a peep.
Read the whole account (scroll down for story).
Try the experiment yourself: Buy a Kerry T-shirt!