1
general::
Remain firmly resolved, as in We're going to hang tough on this point and not give in. This slangy idiom uses tough in the sense of "aggressively unyielding," a usage dating from the first half of the 1900s.
American Heritage Idioms
2
general::
Phrase(s): hang tough (on something)
Sl. to stick to one’s position (on something). • I decided I’d hang tough on it. I tend to give in too easy. • Yes, just hang tough.
McGrawhill's American Idioms And Phrasal Verbs