“I am assuming IF the House approves the bill it has to go back to the Senate, correct?”
As I understand it, it might be sent straight to the president’s desk for signing. According to one school of thought, Pelosi is tricking her fellow rats.
The Senate bill which the House is about the “deem” passed will go straight to Zero for signature. Simultaneously, the reconciliation bill they’ve cobbled together and had scored by the CBO goes to the Senate for, they hope, its approval.
Why the Senate would even want to touch the House reconciliation bill when their bill is about to be signed into law, is beyond me. I doubt they will.