There's no threshold or checklist you can point to as definitive. In fact, one of the most consistent arguments made by loyalists was that the American Whigs had no hard evidence that their rights were abridged in any significant material way. Certainly, not in any way that truly violated the constituted and traditional authority of the British Crown and the Imperial metropole. Rather, what the framers argued was much more philosophical and conceptual than concrete. To be sure, the framers had specific taxes and pieces of legislation they used to bolster their case, but that case always relied on adopting the philosophical framework of classical republicanism.

Now, what is classical republicanism? At its heart, it was a belief in a limited, representative government that allowed for the safe distribution of power amongst those best suited to wield it. It was an Enlightenment political project that sought to move power from an hereditary aristocracy to what was termed "nature's aristocracy," or men of education and means who were best able to wisely exercise political power. One writer described his position, "It is not wealth - it is not family - it is not either of these alone, nor both of them together, though I readily allow neither is to be disregarded, that will qualify men for important seats in government, unless they are rich and honorable in other and more important respects" (Bailyn, 309).

As the name suggests, classical republicanism was derived from the governments and political theories that emerged in ancient Greece and Rome. Now, we should not assume that the American framers and the European Enlightenment theorists had their ancient history right, but instead they cribbed from existing sources to create a political system that they believed would avoid the excesses of the Roman empire and the more recent (and traumatizing to their minds) wars of religion and emergence of the absolutist state. Reading the tracts and pamphlets of the era you see history painted with a broad and dark brush, where heroes like the Roman Cincinnatus are extinguished in nearly two millennia of despotism and intellectual dark ages. A side note, but the framers did not view the Pilgrims and Puritans as forebearers of the new nation, but rather the exact thing they wished to break away from.

The capacity to control and wield political power is really at the heart of all of this. Bernard Bailyn notes in The Ideological Origins of the American Revolution that, "The theory of politics that emerges from the political literature of the pre-Revolutionary years rests on the belief that what lay behind every political scene, the ultimate explanation of every political controversy, was the disposition of power," (55). This is why people like Madison and Hamilton feared democracy. They weren't worried about democracy as we understand it, where people have a voice and a vote for their government, but rather "pure" democracy as they understood Athens, where the passions of the moment could turn political power into an instrument of mob violence. This is also why many of them feared standing armies, strong banking establishments, and corporations (at that time, corporations had charters from governments and typically operated specific monopolies in exchange for tax revenue and kickbacks), Those institutions were accountable only to those who gave them money and authority and lacked the moral grounding in the traditional body politic.

In addition to seeking appropriate leadership and civic institution, the theory of classical republicanism relied heavily on what its adherents called "civic virtue." Civic virtue held that government could only function if the people it represented were virtuous and vigilant. A perfectly structured republican government could slide into tyranny, in this theory, if the people represented by that government allowed corruption. The end result would be despotism. In fact, it was believed that republicanism was impossible without civic virtue. Madison, in a speech to the Virginia Constitutional Convention, argued, "the people will have virtue and intelligence to select men of virtue and wisdom. Is there no virtue among us? If there be not we are in a wretched situation. No theoretical checks, no form of government, can render us secure. To suppose that any form of government will secure liberty or happiness without any virtue in the people is a chimerical idea." Loyalist attacks against the American Whigs argued that, "Not only was the rebellion rupturing the people's habitual obedience to the constituted government, but by the establishment of republicanism the Whigs were also founding their new governments solely on the people's voluntary acquiescence," (Wood, The Creation of the American Republic, 67).

So, what made a government tyrannical to the radical Whigs of the Imperial Crisis? Any constituted government that derived its power from naked force or a tradition of assumed, divine authority was immediately suspect. The British Empire, based on Parliamentary rule and constitutional monarchy in the wake of the Revolution of 1688 was considered a good model to Whigs, but certainly capable of abuse, especially when the traditional rights of self governance in the colonies were limited. The act of taxing the colonies was not dangerous to the American Whigs. The act of taxing the colonies without the consent of the taxed, without set limits for the taxing authority, and without considering the inherent rights of the community being taxed, was seen as a slippery slope to true tyranny.

A final note, governance itself, and the limitations of rights, were not considered tyrannical in-and-of themselves. Saul Cornell noted of the Antifederalist arguments against the Constitution, that even the most radical republicans "accepted the important distinction between unalienable and alienable rights. Certain rights were unalienable and could never be ceded by individuals... Other rights were alienable but could be compromised only when the good of society demanded such sacrifices... Alienable rights were political rights, rights that resulted from the creation of a polity... Limits on liberty were permissible as long as laws were enacted by representatives of the people," (The Other Founders: Anti-Federalism & the Dissenting Tradition in America, 1788-1828, 86). In other words, the Whiskey Rebellion, for example, was not a valid critique of government, since the government was republican in nature, responsive to the people, and acting within its set and constitutional boundaries.