The House passing the Senate bill will make it law once the President signs. However, there are some adjustments the House wants to make to the Senate bill. These would normally have been done in conference committee with both chambers passing the resulting modified bill.
The Massachusetts election left the Democrats with < 60 votes in the Senate, so they can't pass a modified bill there anymore. So the modifications the House wants to the Senate bill will be approved via reconciliation, which requires only 51 votes.