No, not at all. The situation is still all well within the US Constitution in the sense of want people "can do". In particular, as I will outline, there is a very fast, simple solution well within what "the minority can do".
Background: In the US Federal Government, there are three branches, executive (e.g., headed by the president), the legislative (i.e., Congress), and the judicial (with the Supreme Court).
In the case of the Snowden leaks, the actions Snowden was objecting to were by the executive branch which (more or less) was following laws passed by the legislative branch and signed into law by the executive branch. So far so good, that is, within the Constitution. Note that the judicial branch is not involved in passing or signing such laws and so far has not been involved in this whole matter.
But looking at the laws and what the executive branch did that Snowden revealed, a "minority" might conclude that the Constitution was violated. Really, still, so far so good because it's not up to the legislative or executive branch to determine if the Constitution was violated. It's been common throughout US history for the legislative branch to pass laws and the executive branch to sign and use those laws but later the US courts, usually including the US Supreme Court, to find that the laws were "unconstitutional" and strike them down.
So for what a "minority can do" in this case? Sure: Bring a law suit in the judicial branch where the suit claims that the Constitution, e.g., First or Fourth Amendment, was violated. Typically the case (I don't know the details of the process) makes it to the US Supreme Court. For the role of a "minority", in principle only one person need bring the case.
We should guess that people highly concerned with the situation leaked by Snowden will bring such cases. So, we will look for the ACLU and the EFF. But now we also see that Google is bringing a case. The legal costs for bringing a case might be significant, but there are plenty of organizations and individuals with much more than enough money to pay for those costs. Likely cases will be brought.
My guess is that much of the relevant laws will be struck down.
So, why has the judicial branch or the Supreme Court not yet struck down the relevant laws? Because they don't do that; instead, there has to be a legal case brought.
In all of this, the Supreme Court will act very cautiously. And in principle there is nothing important to keep them from acting quickly.
Net, so far the US Constitution is working just as intended. No riots in the streets are needed yet. We just need for some cases to be brought. That the laws mandated a lot of secrecy may have helped slow the bringing of cases, but likely Google, Microsoft, and some individuals have plenty of 'legal standing' to bring suitable cases.
So far the legislative branch passed some laws. They can do that. The laws can later be found to violate the Constitution and even then we don't line up the people in Congress who passed the laws and shoot them. Similarly for the executive branch: Once Congress has passed a law, the executive branch can sign it and use it.
Net, there is only one branch that can say if a law is constitutional or not, the judicial branch, and so far apparently no suitable case has been brought and the judicial branch has yet to speak.
Indeed, I have a letter drafted to my members of Congress but have not sent it because the letter really just claims that the relevant laws were unconstitutional, and for the members of Congress such claims are nearly irrelevant.
Net, we just need a suitable case in the Supreme Court. The Supreme Court will have no difficulty at all understanding all the relevant issues, and that court has plenty of ability to slap down laws passed by Congress and signed and used by the executive branch. Slapping down unconstitutional laws is much of just why the Supreme Court is there, and they are 100% fully aware of that point.
Some of the recent appointees to the Supreme Court are quite 'liberal', but nearly always they are plenty bright and will see the constitutional issues in the activities Snowden described with crystal clarity and intense concern.
The fight over the constitutionality of the relevant laws is not nearly over and, indeed, has yet to begin but apparently is about to begin. Don't bet on those laws coming out whole.
In particular the Constitution says nothing about violating the Constitution with secret orders of the executive branch based on wacko laws and approved by a secret 'court' of persons appointed by a member of the judicial branch with secret oversight by committees of Congress. Maybe the people who dreamed up this wacko nonsense thought that they were clever, but they were not: What they constructed has nothing to do with the Constitution, and the Supreme Court will have no difficulty at all seeing this point.
If the Supreme Court strikes down the laws, they will be gone -- out'a here. And that's just the way the Constitution says the process is supposed to work.
We're a government of laws, not men: What matters are the laws, not what Presidents Bush and Obama say, what General Alexander says, what the FISA 'court' says, or what the Intelligence committees of Congress say. Instead what matters here is what laws the Supreme Court says are constitutional.