The amendment process isn't relevant here. Republicans were completely opposed to any version of Obamacare; amending it wouldn't have fixed matters for them. They were opposed in principle to any large new federal system to make it easier for citizens to buy health insurance.
Are you perhaps referring to Constitutional amendments?
Yes. Constitutional amendments require two kinds of super-majorities just for this reason. Even if technically an individual mandate didn't require a constitutional amendment (I believe it did), the spirit of the amendment process indicates that you should get 2/3 support to propose and 3/4 support to ratify fundamental changes to our government.
The Supreme Court, with a 5-4 majority of conservatives, ruled otherwise. So apparently, it didn't require a Constitutional amendment. At all. A law was plenty.
Are you perhaps referring to Constitutional amendments?