The U.S. Constitution was written, not because people trusted their government to do the right thing back then, but because they did not trust the government. The current political atmosphere, where the government is considered trustworthy until proven otherwise, is a result of Reconstruction and the two world wars that followed. Before that, it was a very real possibility that the newly founded United States might soon devolve into the kind of tyranny that the Founding Fathers perceived British rule to be. The Constitution was an attempt to prevent this from happening. By default, the government could not be trusted; and trust was only granted reluctantly when the government could demonstrate that it was doing the right thing. That's why so many clauses of the Constitution are concerned with what the government can't do. The government was never supposed to enjoy as much blind trust as it does today.
None of this is actually true. The state governments didn't trust the national governments, but the Constitution does nothing to limit the power of government in general (the nearly unlimited power of the state governments, inherited from their status as successors to the British Parliament). The structure of the Constitution is much more about the politics between the states than it is about a blanket mistrust of government.
Look at the state constitutions enacted during the 1776-1787 period, how they were created, and what the public discussion of them was. They show a definite distrust of government. (States may have had regulatory powers, but that did not give them license to be tyrannical by e.g. locking people up without trial or conducting unreasonable searches.) Many of the new ideas that were formed during this period about how to structure state government to hedge against tyranny were also used when drafting the federal constitution.
kijin's point stands: back then people did not trust the government (and a key related point: they knew that even a republican (i.e. democratic) government could be untrustworthy). Much of that healthy distrust is gone today.
The federal constitution naturally only concerns itself with defining the structure and powers of the federal government. The "blanket mistrust of government" that you describe was indeed quite present, and is very much evident in the way the powers of the federal government are constrained and circumscribed by its charter.
Of course the federal constitution doesn't limit the power of already extant state governments; it's not the constitution of any individual state. Each state has its own constitution which charters, and constrains, the powers of the relevant state government, mostly in accordance with the very same "blanket mistrust of government".
There was no "unlimited power of state governments" at all; every state in the union had its own written constitution well before the federal constitution came into existence. Most of them are even more restrictive of power, and more vigorous in asserting protections of individual rights, than even the federal constitution is.
Indeed, the Constitution and Bill of Rights were meant to act as a straight-jacket on the government.
The commerce clause, and numerous laws leading up to it, were the major opening. It made the lobbying boom possible by giving the government direct control over the economy (and therefore lobbyists acquired reason to lobby, and reason to buy politicians).
All powers not expressly granted to the government were to be outside their province. They switched that, such that any powers not expressly denied the government were to be assumed to be in their province.
The Constitution and the Bill of Rights were meant to define the boundary of power between the state and federal governments. All powers not expressly granted to the federal government remained with the states, who had nearly unlimited police powers constrained only by their own constitutions.
What has happened in the meantime is that the civil war and the reconstruction amendments redefined the power boundary between the state and federal governments, but the federal government has not usurped any powers that were originally outside the province of "government" (because there was scarcely such a thing!)
The federal constitution isn't merely there to define the boundaries between state and federal jurisdiction; it's there to define the structure and powers of the federal government itself.
You're trying to argue that the federal government merely usurped powers that the state governments already had, and this is scarcely true. No state ever had unlimited regulatory authority, and no state ever had anything approaching "nearly unlimited police powers"; state constitutions are typically more explicit in restraining the exercise of power than even the federal constitution.