Budge (verb)

1. Move slightly, especially in order to make room for someone or something.
2. Change one's position or opinion slightly.
3. Fail to keep one's promise or commitment.

Origin:

Early 16th century: of unknown origin.

Examples:

1. He refused to budge on the issue.
2. The car wouldn't budge, it was stuck in the mud.
3. The rock wouldn't budge, despite his best efforts.
4. She finally managed to budge the door open.
5. He wouldn't budge an inch on the price.