get (one) over a barrel

To cause one to be in a position of vulnerability, weakness, or powerlessness. Now that we know about his involvement, we've got him over a barrel—he'll give us whatever we want to buy our silence. The seller got us over a barrel, thanks to multiple offers on the house. That's the only reason we went over our budget. If our party can get majorities in both houses, then we'll finally have the opposition over a barrel.

get someone over a barrel

get someone in a helpless position; have someone at your mercy. informal

This phrase perhaps refers to the condition of a person who has been rescued from drowning and is placed over a barrel to clear their lungs of water.