(as) busy as a beaver (building a new dam)

Very busy, assiduous, or hardworking. The phrase refers to beavers' reputation for being extremely industrious. Between working two part-time jobs, volunteering on the weekends, and looking after his little brother, Sam's been busy as a beaver this summer. I've been as busy as a beaver building a new dam this year. I've had almost no free time! Believe me, this audit has kept everyone in the department busy as a beaver for months. We can't wait till it's over!

(as) busy as a bee

Very busy. I'm currently choreographing three plays, so I'm as busy as a bee. Can we meet next week instead? I'm busy as a bee right now. Believe me, this audit has kept everyone in the department busy as a bee for months. We can't wait till it's over!

busy as a beaver/bee

Extremely industrious. The proverbial comparison to bees dates from Chaucer’s time. The one to beavers is newer, going back only to the seventeenth century; it also is put as works like a beaver and eager beaver. Among more recent proverbial comparisons for being busy, which liken it more to nervous overactivity than ambitiousness, is busy as a one-armed paperhanger, an Americanism dating from about 1910.