dig in (one's) heels
To cling stubbornly to one's beliefs or wishes. Please let me tell my side of the story before you dig in your heels on this, OK? Well, I told Grace she can't go, and now she's dug in her heels as if this party is the most important thing in her life.
dig (one's) own grave
To do something that has or will have negative consequences that are easily able to be foreseen. If you don't turn in your project, you're digging your own grave. There's no way you'll get a decent grade without it! I'm afraid I'm digging my own grave by turning down the promotion.