pull in one's horns

Also, draw in one's horns.

Retreat, back down, restrain oneself, as in The town manager wanted higher taxes but public reaction made him draw in his horns. This expression alludes to the snail's habit of drawing in the soft projecting parts of its body when it is threatened. The idea was first expressed in the 15th century as shrink one's horns, and the idiom with draw developed about the same time. The idiom with pull did not appear until a century later.

Reduce expenses, as in That drop in profits will force the company to pull in its horns. [Late 1800s]