but the Senate then needs 60 votes, not 51. Unless the hOuse passes the Senate bill, reconciliation does not apply.
If the House passed the Senate bill, it would go to the President. Why would there be any need for a “reconciliation” rule that only applies to bills passed identically by both houses of Congress? It doesn’t make any sense. Reconciliation is for when one house passes a budget bill that’s slightly different from the version passed by the other house.