Anything other than a simple, direct denial would have been 'leaking' information about the possibility of such a program existing, which is expressly against the law as well.
The NSA programs are either constitutional or not. Wyden was essentially asking, Is this program constitutional? Does it collect data on US persons without a warrant?
Clapper swore an oath to the Constitution, so he should always be able to answer that question truthfully. "Yes, this program is constitutional. No, it doesn't collect data on US persons."
The fact that he couldn't say that is the issue.
Secrecy is not some magic sauce that makes a program constitutional. Secrecy doesn't free a program from legal scrutiny.
The idea that constitutionality, or any other question of legal interpretation, is a matter of objective fact which has a clear, crisp, true or false answer is, while a comforting illusion, not at all even remotely true.
It's pretty hard to square the alleged seizure of all privately transmitted data with the Fourth Amendment.
Attempts to justify it that we've heard about so far, like the assertion that it's not a seizure until the data is "looked at" is clearly a post-hoc rationalization which, put nicely, strains credibility.
"Seizure" would imply the government taking custody of something away from the owner, which is not what's going on during a bitcopy.
Search is closer, but you missed noticing one of the most important words: " ...against unreasonable searches and seizures".
In other words if the search can be construed "reasonable" for any reason (which is very much a "judgment call") then it is automatically Constitutional (even if it's not automatically legal, which can be a separate consideration).
Additionally the NSA is not seizing all privately transmitted data (which is in any event physically impossible). Either they have to be selective about what metadata is retained long-term, or they have to buffer everything but only for a short term in which case they are acting very much like a "common carrier" with an exceptionally bad problem of bufferbloat.
But either way, there's another problem: The data being "searched" isn't your data, it's someone else's data (at a different ISP or host) that happens to be bit-for-bit identical to the data you transmitted, which means any 4th Amendment claim would be theirs to make, not yours. So I would be careful about how strictly you try to read into the Fourth Amendment, as only the "judicial activist" interpretations of it would possibly exclude electronic surveillance of the type now done by NSA.
There is a very wide gulf between those two positions, a gulf where the constitutionality of those programs is up for reasoned debate (e.g., with Sen. Wyden's question).
But Clapper would have responded the way he did since disclosing "methods & means" of electronic surveillance is also illegal, and given the direct nature of the questions by Sen. Wyden could hardly have been properly evaded by the standard "can't confirm or deny" excuse the government always gives. In other words Sen. Wyden employed the same logic as the "warrant canary" you guys all find so fascinating :)
Both intelligence committees submit questions to intelligence agencies in advance, who can then comment on these questions and make requests for change (such as moving some to the closed session). This is done in private, so moving a question to the closed session does not reveal any information to the public.
Even if for some reason this question blindsided him, he could have refused to confirm or deny it in an open session, as others have pointed out. But he wanted to put the PR fires out, and telling Congress and the public that they didn't collect bulk metadata indiscriminately served that end at the time, but later came back to bite him (and hopefully cost him his job, if not more).
Ron Wyden also gave him multiple outs and heads ups before his testimony if he wanted to get out of it.
I think Congress would think that he is legally required to answer them truthfully, not to lie, and would be appalled at the suggestion that anyone could be legally required to testify falsely to them.