> I'd say there's nothing that the minority can do (if it matters I'm not from the US)

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.