He knew it could damage his career, but Keith went out on a limb and said he supported the anti-war protesters.
I don't think that saying you support gay rights means you're going out on a limb these days.
Origin: Probably metaphorical, from the fact that if you're climbing a tree and you go too far out on a limb, you're taking a risk because the limb could break and you could fall to the ground and hurt yourself.
