Yes, they did have varying opinions, I'll describe a bit about George Washington, Thomas Jefferson, and Alexander Hamilton, while touching on James Madison.

The 'original' split, per se, can be traced to a difference of opinions between Alexander Hamilton/the Federalists and Thomas Jefferson/the Democratic-Republicans: they disagreed over issues such as how the remaining Revolutionary War debt should be paid, whether bonds for soldiers should be paid out like bearer bonds to their holder or only to the original person it was assigned too, and, most importantly, the economic direction of the country.

Jefferson imagined an agrarian nation of independent landowners and farmers with a weak federal government; Hamilton preferred a mercantile economy which would demand more federal power and a stronger centralized government. Jefferson and James Madison are actually responsible for the original doctrines of states rights and nullification, the former of which still bites us in the ass today, and the latter of which became a major point of contention during Andrew Jackson's administration and also contributed to the Civil War.

George Washington kept both Jefferson and Hamilton in his cabinet for his first term (Secretary of the Treasury Hamilton, Secretary of State Jefferson) and attempted to mediate their disputes, but he was the last really 'independent' president (though Ron Chernow makes a strong argument that he may have leaned a pinch toward federalism). Anyway, in his farewell address, Washington gives a very specific and damning warning about the dangers of political parties: in essence, he felt people began to affiliate with their party over their nation.

They serve to organize faction, to give it an artificial and extraordinary force; to put, in the place of the delegated will of the nation the will of a party, often a small but artful and enterprising minority of the community; and, according to the alternate triumphs of different parties, to make the public administration the mirror of the ill-concerted and incongruous projects of faction, rather than the organ of consistent and wholesome plans digested by common counsels and modified by mutual interests.

The alternate domination of one faction over another, sharpened by the spirit of revenge, natural to party dissension, which in different ages and countries has perpetrated the most horrid enormities, is itself a frightful despotism. But this leads at length to a more formal and permanent despotism. The disorders and miseries which result gradually incline the minds of men to seek security and repose in the absolute power of an individual; and sooner or later the chief of some prevailing faction, more able or more fortunate than his competitors, turns this disposition to the purposes of his own elevation, on the ruins of public liberty.

Edit: Sources:

Hamilton, by Ron Chernow

The Art of Power by Jon Meacham

Washington: The Indispensable Man by James Thomas Flexner

The Portable Thomas Jefferson

Papers of George Washington/Alexander Hamilton/Thomas Jefferson/James Madison