Before we get to the answer, let's carefully articulate the question.
First of all, what is metadata?
Metadata is summary information about communications. Generally it includes (1) the calling number, (2) the receiving number, (3) when the call was made and (4) how long the call lasted.
Note that one cannot tell with absolute certainty from metadata who actually talked to whom but one can establish a fairly high probability. Nor can one know what was said. One only knows the duration of the call.
This information is generally the property of the service provider and not the property of the people communicating.
Second of all, what's the so-called reason for the collection? The NSA claims it's to protect against terrorist activity.
Finally, the Article of the Constitution that it may be violating is Amendment IV which states "The right of the people to be secure in their persons, houses, papers and effects against unreasonable searches and seizures shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
Now, clearly the NSA had no warrant "particularly describing the place to be searched, and the persons or things to be seized."
They were scooping up information wholesale. So how the hell could this possibly be Constitutional?
For two reasons. The first is that, as mentioned above, the information collected is not the property of the caller or person being called. It's the property of the service provider and they apparently freely provided this information.
If you don't know that using the telephone, sending an e-mail or logging on to the internet is being recorded by someone, somewhere and then that information is being used to sell you stuff or send you offers, you're an idiot or you're not paying attention.
So why should you have any expectation of privacy at all when engaging in these activities? This is certainly a question that will be raised during the court case. Now one could claim that this metadata is a "paper" or "effect" or that one does not surrender expectations of privacy when using the provider service. I suppose we'll see.
The other issue is the word "unreasonable." What the hell is an "unreasonable" search or seizure?
Normally it's a search or seizure without "probable cause." And what is "probable cause?" It's knowledge or information that would lead a reasonable person to conclude that a crime is being committed, has been committed or is about to be committed.
Obviously, when you are collecting every piece of information available, you cannot possibly have "probable cause" for everything you're seizing.
So, is there any exception to the "probable cause" requirement?
Yes, there is. In two Supreme Court decisions, U.S. v. Martinez-Fuerte, related to roadblocks to check for illegal immigrants, and Michigan v. Sitz, related to DUI checkpoints which stopped all or random vehicles to check for driver intoxication, the SCOTUS balanced "state interests" against "4th Amendment protections" and concluded that the interests of the state outweighed the minor 4th Amendment inconvenience of the seizure or stopping of vehicles with no particular probable cause related to that vehicle.
In other words, the seizure was not "unreasonable" despite the lack of "probable cause." However, the court made it clear that a "search" still required "probable cause" such as a driver smelling of alcohol at a DUI stop.
So, now we have to differentiate between the "seizure" of the metadata and the "search" of the metadata. I'm not even sure that such a distinction in this case can be made but, assuming it can, then I can see an argument along the lines of the "seizure" being in the state's interest to protect against terrorism but the "search" of the data requiring probable cause.
Of course then the agency would have to demonstrate to a court that this wholesale gathering of information is an EFFECTIVE method to combat terrorism which they may or may not be able to do.
Just about every agency and board that has reviewed the NSA activity has concluded that it's unconstitutional and one court has said that it is probably unconstitutional as well.
The NSA is far and away the most arrogant agency I've ever had the misfortune to interact with but they also have lots and lots of very smart people with lots of access to lots of things that we don't know about.
The Roberts Court also strikes me as one that looks for legal excuses to do what they want to do anyway. It really wouldn't surprise me if by the time this thing got to the Supreme Court they didn't have some sort of excuse to say it's OK if they want to say that.
I also don't count out the NSA presenting classified evidence in closed sessions, real or fabricated, that the public won't hear about for 50 years. In other words, despite everyone being so sure that this violates the 4th Amendment, it wouldn't surprise me at all if the SCOTUS said it didn't.