To speak of a "republican" tradition in contradistinction to Locke's "liberalism" is important because many scholars after most notably Bernard Bailyn argued republicanism prevailed over liberalism. I am suspicious of this claim and have concluded there were simply viable streams of thought that were in tension with one another (harmonized as unified by the "Whigs").
Likewise with egalitarian republican Rousseau. He wasn't popular in America. But both present day America and Europe have similar safety nets, redistribution of wealth and income, and regulations on businesses, with Europe tending to be slightly more progressive. A difference in degree, not kind.
Late 18th Century England and America may not have cared for Rousseau, but they did have their own stream of "republicans" who argued for economic leveling on very similar grounds. They tended to do so using biblical language. However, Rousseau was, at least exoterically, a theist who claimed to be a Christian.
So we can swap Harrington for Rousseau, and it doesn't make much of a difference.