Never mind that Romney's legacy has been plagued by cost overruns since it started. Other surveys show that the majority of people like the provisions in the ACA that, for example, eliminate screening for pre-existing conditions by insurers, and that force businesses with more than 50 employees to either provide insurance or pay a penalty.
The one part the majority consistently opposes: the individual mandate, the constitutionality of which the Supreme Court has yet to rule on. Once you give something to people, especially when it absolves them of some responsibility, it's hard to take it back.
Finally, to stay in power, Republicans would likely have to replace the ACA with something else. After all, with apologies to Ernest Hemingway, the existing "system" was first slowly, then quickly, bankrupting us as a nation. If we do go back, where does that leave hospitals and health systems that have invested copious amounts of time, money and talent into readying and reinventing themselves for the changes? I'm not sure, but I can guarantee it would be a very bad place.
So for all these reasons, and despite all the bloviating about healthcare from your national candidates for the office of president, don't believe it. I don't think they do.