So when Trump says, "I like the mandate", how was that statement massaged and distorted? It is right in line with Trump's statements back in August where he said the uninsured would have their medical bills paid by the government. With no mandate in place, everyone drops their insurance in order to get their bills paid by the government. Of course Trump would want a mandate. Which is why he said, "I like the mandate".
The idea aka the mandate - is the Republican party idea dating back to Ronald Reagan when in 1986 he signed a law that requires hospitals to treat poor people and undocumented immigrants universally. This became the Dole plan and then onward to Romney care. All Republican plans - ideas thought up by Conservative think tanks like Heritage Foundation.