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:

“…little screws of steel were made use of, that screwed the thumbs with so exquisite a torment, ... And, upon his refusing to take it, they put his thumbs in the screws; and drew them so hard, that as they put him to extreme torture.”

Putting the screws on was used somewhat metaphorically by February, 1842, when it appears in Dublin University Magazine, in the serialized novel, "Gasper the Pirate: A Tale of the Indian Seas," chapter VIII:

“‘Shall we put the screws on?’ suggested another, as the man remained   silent and unmoved.” 

At the bottom of the page it is noted: "Putting the screws on is a cant term for applying any kind of torture."

Use of "put the screws to" in a purely figurative connotation was around by July, 1870, when it was used in the college paper, The Dartmouth in "Exchanges:"

“I did not mean to insult him. I did mean to put the screws to him for his own good. The only way to bring some people out of the depths of ignorance, is to put the screws to them, and if a man has a sound foundation it never hurts nor insults him.”                                                           

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