Douglas campaigned on bringing in medicare in the 1960 election; they won a majority government, but only 40% of the popular vote (the main opposition parties weren't ferociously opposed, but not in favour of implementation either.)  The doctors coalesced opposition before and during their strike.

Was the province as a whole in favour of medicare?  I'd say yes, but it was far from being a consensus.

Read Evildoer's two comments above about how far it was, and the aftermath.