That is what the pundits call a “sever-ability” clause. If you cannot parse it then the entire thing is dropped.
The Supreme Court has ignored a lack of a severability clause before. Not a lawyer, so can’t quote cases. So don’t count on the whole thing being struck down.
I give about 90% odds on the individual mandate being struck. And 95%+ on the rest of the bill standing, based on the current makeup of the Court. 5-4 to strike the mandate, and 6-3 or 7-2 in favor of the rest of the law. Thomas will strike down the whole law, and I expect Alito to do the same. Not sure about Scalia, and think Roberts and Kennedy will defer to Congress.
If Congress defunds implementation of the law, I expect that also to stand, until the Demonrats take Congress again. Unless we get a solid conservative President, I expect a Republican President to fold. Cain, Paul, and Bachmann would veto funding. Have no clue what Perry and Romney would do if facing a Demonrat Senate. My guess is fold, but maybe they would choose avoiding being primaried in 2016. Maybe.