What do we mean when we say it today?
This one hasn't changed much over time. People won't "budge an inch" when they're standing firm.
Sometimes this is said in the context that Sly says it: meaning a person literally won't move at all. But most of the time this is said figuratively, as in, someone won't change his or her position on something. His mind is made up. She is certain of what she thinks and she's sticking to it. You get the idea.