Budget expert Sarah Binder explains the reconciliation process:
[K]eep in mind that when/if the House and Senate pass different versions of a reconciliation bill, Republicans could still filibuster the three motions to go to conference (even if they couldn’t filibuster the actual conference report that might emerge). If it gets to that point, expect the House and Senate to play a little ping pong as they try to get to a final agreement. So, no, nothing regarding reconciliation is as simple or as fast as it may be seem. “If you want something done quickly, don’t send it to the Senate.”
I think the House Dems should have enough balls to pass the imperfect Senate bill as is.