Funding Obamacare is a promises that the 111th congress made that the 112th congress won’t keep. The Obamacare law will be on the books but about as enforceable as the Alien and Sedition Acts were after the Anti-Federalists were swept into power.
Until the law is repealed, they will have to fund it. They can slow down the funding and the implementation of the law, but repeal is necessary. It is the law.