Uh, no.
The point of the 4th Amendment is that it protects against *warrantless*
searches and seizures.
Now you can *challenge the subpoena* on those grounds (that the warrant is
improper according to the 4th Amendment). What you can't do is pocket-veto
the subpoena.
It is exceedingly dangerous to ignore a subpoena under ANY set of
circumstances. The appropriate choices of action are to either comply with
it or fight it, but you must NEVER ignore it. If you DO ignore it, you risk
the judge who signed the subpoena issuing a bench warrant for your arrest on
either civil or criminal contempt charges. The cute part about contempt of
court is that you can be locked up for what basically amounts to an
indefinite period (until you comply with the court's orders) or fined
hideous amounts of money with essentially no recourse. As a rule of thumb,
do not screw around with men and women in black robes behind a bench!
If you don't have what they want you still have to respond.
Let's say you get a subpoena for (A), (B) and (C).
You have (A), but not (B) or (C).
You produce (A), and for (B) and (C) you instead produce an affidavit which
says that no responsive reply is possible as the materials and/or documents
you have been asked for do not exist.
Note that lying about (B) or (C) constitutes perjury, a felony, so don't do
that!
Subpoenas are no big deal. We get them with some regularity (probably two
or three a year) around here. Usually it is the result of some investigation
that is being done on either a civil or criminal matter where someone did
something that another party or the government doesn't like (ie: forgery of
a purchase order or check, etc). We're on a good enough basis with the
local Federales that when they're going to send one of these over they
usually call first asking for what they want; we point out that our policies
and contract prohibit disclosing what they want, and they very politely say
"thank you very much". An hour later a nice man appears with papers in
hand, signed by a judge - at which point we give them exactly what they
asked for. 
I've yet to fight one that we've received at MCSNet, but if I felt there was
good cause to do it, I would.
Unless you have a contractual duty to your customers not to comply with a
subpoena (not unheard of in a contract, but also unusual) you do NOT have
to notify them that you were served or give them the opportunity to quash
the subpoena.
If you EVER get one of these and suspect, for any reason, that it is aimed
at *you*, don't do a thing until you talk to a GOOD lawyer - and do that
RIGHT AWAY. Most subpoenas have to be complied with or fought quickly -
if you're lucky you have five business days. Sitting on it for any length
of time is a very bad idea.
The kind of thing being talked about here though, where someone wants copies
of *backup tapes*, could easily be aimed at *YOU*. It also might not be
though - generally, when you get one of these and its aimed at a third party,
the reason for that kind of request is that in order to be admissible the
records must be produced in the "ordinary course of business". Ergo, if
a customer is doing something "bad", and they think you have a copy of it
on a backup tape, they can't ask you to extract the contents of THEIR
directory, because doing that is not an ordinary record - and further, it
leads to questions about the custody and control of the information.
Instead, they'll ask for the whole tape and have one of their forensics
people dissect it to get the information they want.
Note that, as others have noted, if the subpoena is from a grand jury, you
won't be told much when you inquire as to what's going on (other than that
it is from a grand jury). The reason is that grand jury proceedings are
held in secret, and it is a crime to disclose the proceedings in the grand
jury room until they are concluded.
None of this is legal advice, since I ain't a lawyer