It's kinda funny that people can call something a "Republican" or "Democrat" idea because they can point out a Republican or Democrat who had a similar idea at one time.
The mandate has had supporters and opponents on either side of the aisle. Obama pretty vehemently opposed it (when it was Hillary's idea) before he supported it. Just like some Republicans supported it at one time, although there was always opposition.
It only becomes hard to reconcile if you view yourself and others in terms of what team they're on. As if people can only check off on one laundry-list of party ideas or the other, and not weigh each individual issue on its merits.