They will have to veto the whole thing because its all or nothing according to the Constitution. In fact, the Congress had a provision in the bill that said the Supreme Court did not have the power to veto all of bill, which is a direct violation of the separation of powers. This should make any self respecting justice rule against this immediately, but you never know with some of the, like Souter.
I'm not sure how its exactly worded. I've been attempting to read the legislation tonight, but as usual, you have to be a lawyer to undertsand most of the finer points, as they relate existing law. But if I'm not mistaken, it's quite proper, for certain parts of this CFR legislation to be found unconstitutional by the USSC, while other parts can be deemed constitutional. At least that's the way I understand it to be.
Check it out here. Plug "HR 2356" into the number box.