The Republicans' second attempt at repealing the Patient Protection and Affordable Care Act (PPACA or "Obamacare") is failing. As such, the current president wants the PPACA to "fail" if his party can't repeal it:
He smugly declares "I'm not going to own it" and "I can tell you the Republicans are not going to own it.", but if the PPACA fails, it will be the fault of him and his party. They're the ones in charge, not President Obama and the Democrats; if Republicans poorly handle the government that they're running, the buck stops with them.