We have called by different names brethren of the same principle. We are all Republicans, we are all Federalists. If there be any among us who would wish to dissolve this Union or to change its republican form, let them stand undisturbed as monuments of the safety with which error of opinion may be tolerated where reason is left free to combat it.
The famous second sentence of that passage embodies a sort of pun. The Republicans (later Democratic-Republicans, later Democrats) were Jefferson’s partisans: Southern, agrarian, egalitarian in principle, Francophile, skeptical of the powers of the national government. The Federalists were the party of Adams and Hamilton (who nonetheless hated each other): Northern, mercantile, elitist in principle, Anglophile, worried about making sure that there was a national government with adequate powers to bind the nation together.
So, written with capital letters, Jefferson’s statement was false: His hearers were Republicans and Federalists, but no one was both. Written with small letters, his statement was largely true, though much of Jefferson’s campaign, run by Madison, had been devoted to denying it. Republican papers and speeches accused Adams of monarchical ambitions and the Federalist party of aristocratic aims, and hammered (properly) at the Sedition Act as a threat to civil liberty.
Unpacked, Jefferson’s rhetoric meant that both parties were republican in the sense of supporting republican institutions and federalist in the sense of supporting the federal government as established by the Constitution. (The Republicans had absorbed the old anti-Federalist faction that arose in connection with the ratification debates, but there was no significant sentiment among the Republicans for going back to the Articles of Confederation.)
So the equivalent of Jefferson’s unifying theme might be expressed tomorrow more or less this way:
We have called by various names brothers and sisters of a single principle.
If a republican cherishes free government under law, we are all republicans.
If a democrat believes that the voices of all the people should count, we are all democrats.
If it is conservative to defend the Constitution, we are all conservatives.
If it is liberal to love liberty and hate tyranny, we are all liberals.
If a progressive dreams that tomorrow will be better than yesterday, we are all progressives.