Yes, there were political parties in Colonial America. My expertise is in New York history, so I will confine my answer to that, so maybe someone else can fill you in on the rest.

As you may know, New York was originally a Dutch colony that was taken over by the English in 1664. But the takeover wasn't altogether peaceful, as the Dutch increasingly saw the English undermining their way of life. The treaty handing over New Netherland to the English agreed to allow religious freedom to continue to exist in the colony, for example, but the English almost immediately began levying taxes against all the colonists to pay for the clergy and buildings of the Anglican church.

The Dutch ended up re-conquering the colony briefly in 1673, but the English took it back in 1674, and kept it for a hundred years.

But by the 1680s, the relationship between the Dutch farmers and the English government had deteriorated enough that there was a rebellion. This was called Leisler's Rebellion because it was led by a New York Assemblyman named Jacob Leisler.

Leisler and his forces took over the fort at the south end of Manhattan, then called Fort George. The fort included the colonial treasury, so the forces essentially took over the finances for the colony.

This was all peaceful; there were no shots fired and nobody was killed. But the English Navy was notified, who then sent ships down to Manhattan to put down the rebellion.

This, too, was done mostly peacefully. A shot was fired but nobody was killed and Leisler and his forces agreed to relinquish control after some of their demands were met.

But then the English governor of the colony, Henry Sloughter, put Leisler and his son-in-law to death. They were hanged in the public square, not far from where the New York Stock Exchange now stands, and this upset the people of New York a great deal. Nobody had been killed in the actual rebellion itself. Jacob Leisler's punishment did not seem to fit the crime.

The aftermath of this was that New York politics for the next ~40 years was divided into two political factions that were known as the Leislerians and the anti-Leislerians. The Leislerians tended to be middle and lower class farmers, particularly those who spoke Dutch. The anti-Leislerians were middle and upper class merchants and other New Yorkers, particularly those who spoke English.

These divisions eventually gave way as the Dutch population of the colony diminished in relation to the English population. By the 1750s, New York politics was divided in a way that paralleled the divisions back in Britain. The "Whig Club" formed in New York in 1752, led by local aristocrat William Livingston. The more conservatives Tories, then, were led by another local aristocrat, Oliver Delancey.

The Livingston and Delancey families both became political dynasties, and they have often been written about as a microcosm of New York politics in the lead up to the American Revolution. Livingston's Whigs were the Patriot party, pro-America and pro-Continental Congress. Delancey's Tories were just the opposite. When the war broke out, Oliver Delancey joined with the British forces and raised Loyalist regiments to fight against George Washington and the Continental Army.

That all said, the political parties of that era weren't officially organized as they would become later on under Andrew Jackson and Abraham Lincoln and others. There were definite political factions who would side with each other over issues, but there wasn't anything like a formal party structure with a published agenda trying to get a platform enacted or legislation passed or anything like that.

And again, this only applies to New York. The political situation was different in each of the colonies, and national politics didn't really arise in the soon-to-be-United States until the aftermath of the French and Indian War and the run-up to the Revolution.

FURTHER READING:

Colonial New York: A History

The Whigs of Colonial New York

Gotham: A History of New York To 1898

Leslie's History of the Greater New York