Originally "put the screws on, this is a hyperbolic idiom meaning to apply extreme coercive pressure on someone. It is taken from the 17th century torture method where metal screws were used on a prisoner’s thumbs, as described in Bishop Burnet’s "History of His Own Time; From the Restoration of King Charles II to the Conclusion of the Treaty of Peace at Uthecht in the Reign of Queen Anne" by Gilbert Burnet published in 1809, page 253:
Where Did That Come From? - Put the screws to someone