"We will pass a bill that will keep the government open, that will reflect the House's wishes, that will have fundamental changes to Obamacare"
The idea which is gaining traction in some Conservative Circles is to strike at the heart of ACA Law by delaying "individual mandate". By depriving participation of 'healthy individuals' in these insurance pools; these willy business minded conservatives are basically aiming to 'sabotage' ACA from inside. So expect Monday night a third iteration from House GOP members - a bill which allows ObamaCare but without "individual mandate" in response to a return bill by Senate on Monday. Again Senate and Obama White House cannot fall for such tricks even though few Red State Democratic Senators would fall cheaply for such traps (the weakest link in united Dem front) .
House GOP wants to keep playing this pin-pong. In a way they are loath to admit the defeat on ACA. Until that acceptance happens, Federal Gov. will remain closed while like a parrot House GOP will keep repeating that "they will not shutdown the government". That is just a cover to hide their machinations in engineering precisely such a shutdown. May be once many Republican House Members are able to demonstrate the inevitability of ACA to their 'base'; they will get a respite from a Tea Party backlash as they would have tried everything humanly possible to stop this law by then. That could be the point when this log-jam may resolve.