No, the house must reject whatever the senate sends back to them and then send a new “clean” CR funding the entire government, except with ZERO funds for the departments charged with implementing Obamacare. And I believe that would be maily HHS and IRS. The senate will object, then they can negotiate the proper funding levels for those departments again, with zero funding for obamacare being approriated.
Yes, the House should reject anything from the Senate that doesn't match what the House just passed - which explicitly defunds Obamacare. If the Senate chooses a government shutdown, so be it. We'll starve the big-government beast until the Democrats vote to defund Obamacare. During the shutdown, however, the Democrats will continue implementing Obamacare as outlined in the CRS report. I'm not supporting that or saying it's legal. I'm saying that's what they'll do.