But "spare me" is definitely old-fashioned, and something that I would rarely say, if ever. Oh, maybe in dismissing someone I'd say, Oh really, please spare me the details.
Howbout: Let me out of it [my commitment]. What can I do to get out of this?
Regardless, it's definitely not something to say unless you're ten years old. (But I agree, it would be hilarious to hear a Russian say that just because it would be so cute)