I’m guessing that the paragraph you’re referred to is this one, from Barr’s speech to the Federalist Society:

The grammar school civics class version of our Revolution is that it was a rebellion against monarchial tyranny, and that, in framing our Constitution, one of the main preoccupations of the Founders was to keep the Executive weak. This is misguided. By the time of the Glorious Revolution of 1689, monarchical power was effectively neutered and had begun its steady decline. Parliamentary power was well on its way to supremacy and was effectively in the driver’s seat. By the time of the American Revolution, the patriots well understood that their prime antagonist was an overweening Parliament. Indeed, British thinkers came to conceive of Parliament, rather than the people, as the seat of Sovereignty.

Barr is half right, but the half he gets wrong suggests a distorted understanding of the significance of he American Revolution.

Though Barr is correct in saying that the monarch’s powers were greatly reduced at the time of the American Revolution, George III was still, at least in theory, an extremely powerful figure. In his Commentaries on the Laws of England, written in the period immediately before the American Revolution, William Blackstone describes the supreme power of English government as being “divided into two branches; the one legislative, to wit, the parliament, consisting of king, lords, and commons; the other executive, consisting of the king alone.” The king was furthermore, theoretically, “not only incapable of doing wrong, but ever of thinking wrong: he can never mean to do an improper thing: in him is no folly or weakness.”

While Parliament held most of the actual power, this legal theory had practical consequences for those who took issue with the government. Pauline Meier writes in her book American Scripture: Making the Declaration of Independence:

In British politics, accusations of misgovernment were customarily leveled against the King’s ministers even if there was strong reason to think that the King was personally responsible for the actions of his government. The King remained above politics, an incarnation of the state and its continuing legitimacy. Accusations were extended to the King only when grievances had become so general, and evidence of his complicity so unmistakeable, that the authority of his government had come into dispute. To attack the King was, in sort, a constitutional form. It was the way Englishmen announced revolution.

When the Revolutionary War began with the first shots at Lexington and Concord on April 19, 1775, it was still a rebellion fought under the Crown, not against it. Barr’s right to describe the colonists at this point as fighting against George III’s ministers rather than the king himself. This understanding of the conflict is well-depicted in a January 1775 cartoon by Paul Revere title “A Certain Cabinet Junto,” which depicts a speechless king manipulated by ministers who conspire against American liberties. In the so-called “Olive Branch Petition” of July 8, 1775, the colonists affirmed their loyalty to the king, and justified their rebellion, writing “Your Majestys ministers persevering in their measures and proceeding to open hostilities for enforcing them, have compelled us to arm in our own defence, and have engaged us in a controversy so peculiarly abhorrent to the affections of your still faithful colonists...”

But as the war went on, Patriot opinion turned more and more against the king himself. George III didn’t help his case when, in a speech to Parliament on October 26, he denounced the rebellion and called for “a speedy end to these disorders by the most decisive exertions.” According to Meier, Congress received news of this speech on January 8, one day before Robert Bell began distributing copies of Thomas Paine’s Common Sense in Philadelphia.

Thomas Paine not only inveighed against King George III, but against the British monarchy in general, writing:

The prejudice of Englishmen, in favour of their own government by king, lords and commons, arises as much or more from national pride than reason. Individuals are undoubtedly safer in England than in some other countries, but the will of the king is as much the law of the land in Britain as in France, with this difference, that instead of proceeding directly from his mouth, it is handed to the people under the more formidable shape of an act of parliament. For the fate of Charles the first, hath only made kings more subtle—not more just.

No longer was the king an apolitical ruler manipulated by conniving ministers. Now he was a tyrant, ruling despotically through a puppet parliament. In a resolution dated May 15, 1776, Congress formally declared their opposition to the king himself, resolving that “it is necessary that the exercise of every kind of authority under the said crown should be totally suppressed, and all the powers of government exerted, under the authority of the people of the colonies.” On June 7, Richard Henry Lee proposed the Lee Resolution, declaring “That these United Colonies are, and of right ought to be, free and independent States, that they are absolved from all allegiance to the British Crown, and that all political connection between them and the State of Great Britain is, and ought to be, totally dissolved.” The Lee Resolution was passed on July 2, and the final wording of the Declaration of Independence was approved on July 4.

In short, Barr’s claim is misleading. However the revolution may have started, it very quickly became a war against the king and for republicanism. Tellingly, they did not establish a new monarchy after the war, and the executive branch they eventually settled on would remain unusually weak until the twentieth century.

EDIT: Edited for grammar and spelling.