Should the gop be willing to shut down nonessential govt functions to stop obamacare?
False choice. Congress is capable of fully funding government except for Obamacare. No shut down would be necessary. Of course, the Senate will likely add Obamacare funding back in and send it back to the House. Nothing says the House can't remove Obamacare funding again and sent it right back.
Point is, no govt functions need stop to de-fund Obamacare. It would be on Reid and the Dem controlled Senate if they refused to vote for a funding bill that kept the government going ex Obamacare. Why the establishment RINOs think they'd be blamed is beyond me. As you say, they have no backbone!
This is what I think will go down. The Senate will send a continuing resolution bill funding the government including Obamacare to the house and the House will either pass it or be blamed for shutting the government down. That is the advantage the Senate has gained by illegally refusing to pass a budget sent to them by the House.
The operative word is Illegally.