Not a republic, not technically, but the English Parliament, no doubt. Bicameralism, impeachment, an executive cabinet--these did not exist in the Roman Republic.

Of course, English democratic tradition was influenced by Rome's. As was America's. But it's a stretch to say the U.S. was "modeled" on the Roman Republic. It was a new system of government. (If one were to claim it was modeled on anything, it would have to be the English government.)