The central idea, the individual mandate, came from a 1989 lecture by Stuart Butler, an economist at the conservative Heritage foundation. It originated as a conservative alternative to socialized healthcare.
But in politics, the idea was pushed by democrats. The idea that Republicans came up with RomneyCare is simply false, it never would have happened if the Republican Party controlled Massachusetts. Look at actual republican controlled states and you can see what they did on health care pre-ACA and it was pretty much nothing.
People at conservative think tanks coming up with an idea doesn’t make it “republican”. In reality the party ignores many things that the heritage foundation or various other foundations or think tanks say, they’re much more focused on politics than on ideas.
The Heritage Foundation is the flagship conservative think tank, Republican and conservative are synonymous in popular usage, so yeah I think it's safe to call their proposals Republican proposals despite the fact the party can't actually enact all of them.
And if we skip ahead 4 years to 1993, a Republican Senator introduced, a bill with 20 Republican co-sponsors including Bob Dole, Orrin Hatch, and Charles Grassley called the HEART bill.
That bill included an individual mandate, vouchers for low income individuals, and protection for prexisting conditions.
Not all Republicans supported this plan, but almost half of the Republican Senators including most of the leadership supported it. I'd call that a Republican plan--a plan based squarely on the proposal from the heritage foundation.
