Strict constructionism is much different from originalism. The former is about rigid interpretation of the language, while the latter is about divining intent of the framers. Intent gives more flexibility, eg, reading freedom of "speech" & the "press" as being more than just the spoken word or printed material. The Constitution's author's intent would be free communication, eventually including media not envisioned at the time. A strict constructionist would lean towards more limited protections.
It seems more likely that an originalist would strike down the entire ACA, since the Constitution doesn't grant the authority for the fed to impose such a requirement on companies.