Yup, the authors of Obamacare forgot to include severablity language.
Yup, Congress passed it without amending such language into it.
Yup, the President signed it without such language.
Yup, that means if you strike anything you're striking the whole thing.
I know you're used to that language being in every single law, but it's not there this time.
Do your duty. If something is unconstitutional, you must strike it. Even if that means taking out a huge portion that is constitutional without the struck portion.
It really is simple. It's only complicated if you make it so, it is not inherently thus.