“Legislation is supposed to originate in the House...”
Just a nit-pick here. Legislation can originate in either house, except for bills that raise revenue which must originate in the House of Representatives. However our betters have figured out a way around this, the Senate takes a bill passed by the House, strips it of its content, substitutes a spending bill and sends the ‘amended’ bill back to the House for reconciliation.
Not a nitpick-you are correct. But no matter where they originate, they have to go back to be passed, as you said.
Thank you for the clarification-I was speaking in simplified terms...:)