One sentiment which united the Whigs was "republicanism" was the best if not only viable form of government. Certainly it was preferable to monarchy. The notion of republicanism traces to Western Civilization's Greco-Roman heritage. And the Founders who wrote the Federalist Papers, adopting the surname Publius, imagined themselves as revived Roman republicans. Noble pagans, if you will.
There was another stream of thought which argued that the Ancient Hebrews had a "republic." Eric Nelson's magnificent work traces the intellectual lineage of such sentiment. We see this sentiment represented in sermons such as Rev. Samuel Langdon's The Republic of The Israelites An Example To The American States, (June 5, 1788) and even in Thomas Paine's Common Sense.
I remember reading John Adams' rejection of Paine's argument that the Ancient Hebrews had a "republic." American Creation commenter Lex Lata reminded me. As Adams wrote in his autobiography:
"I told him further, that his Reasoning from the Old Testament was ridiculous, and I could hardly think him sincere. At this he laughed, and said he had taken his Ideas in that part from Milton: and then expressed a Contempt of the Old Testament and indeed of the Bible at large, which surprized me."Yes, as Eric Nelson discovered, John Milton was one of those figures who posited the concept of a Hebraic republic.