Obviously, you didn't read a single link I posted.
Heritage and Romney were explicitly and unquestionably supporting every major feature of what went into the ACA: individual mandates, Medicare expansions, health insurance exchanges, subsidies on health insurance, requirements for insurers to accept pre-existing conditions and so forth. They supported Romney's reforms, it was unquestionably a bipartisan effort, and iirc had representatives when it was signed into law.
Every major component of the ACA was developed by conservatives and Republicans, notably Romney, and the impetus was to offer a free-market solution. Their goal was to stop people from freeloading off the system (e.g. only getting health insurance when they need it).
It is screamingly obvious that "this should not be a federal law" is a very small part of the criticism of the ACA. Republicans are not shutting down the government because of the principles of federalism. They are openly targeting the parts of the law whose origins were developed by conservatives, as a free-market solution.
Most, I'm sure, genuinely believe it's a bad policy -- despite the fact that none of their dire warnings have come to pass in MA. However, I'm pretty sure that their abject hatred of Obama, and failure to accept that they lacked the votes to elect a Republican president, all play into their beliefs and emotions on the matter.
The question is not "who vote for it." The question is "who came up with the idea, and what were their motivations?" The answer is "conservatives" and "offer a free-market solution."