At least not in the case of call logs or email logs being collected as metadata. Here's the explanation of the relevant court cases:
In the modern world, the Court held, a bugging device on the outside of a telephone booth or a wiretap on a telephone constitutes a “search,” even though they involve no physical intrusion into a constitutionally protected place, because they violate our “reasonable expectations of privacy.”
But Katz immediately gave rise to the question: What is a “reasonable expectation of privacy”? Suppose X has a conversation at a dinner party at which he reveals certain information about himself to the other guests. Thereafter, the government subpoenas one of the guests and compels her to testify about what X told her at the party. Is this a “search” within the meaning of the Fourth Amendment?
In a series of decisions in the years after Katz, the Supreme Court said “no.” As the Court observed in Katz, “what a person knowingly exposes to the public is not a subject of Fourth Amendment protection.” Thus, as a general matter, one has no “reasonable expectation of privacy” when one reveals information to third parties. Because those individuals are free to tell others what they were told, the speaker has no “reasonable expectation” that such conversations are “private.”
In United States v. Miller, decided in 1976, the Supreme Court considered the following question: Is it a “search” within the meaning of the Fourth Amendment for the government to subpoena information from a bank about a depositor’s financial transactions? Surely, one’s financial transactions are “private,” right? The Court said “no.”
Because the depositor had “voluntarily conveyed” his financial information to the bank and its employees,” who were complete strangers to the depositor, the depositor assumed the risk “that the information would be conveyed by the bank to the government.” Hence, the Court held, the depositor had no “reasonable expectation of privacy” in the information and there was therefore no “search” of the depositor when the government obtained the information from the bank.
Three years later, in Smith v. Maryland, the Court extended this logic to a pen register, a device that collects all the numbers called from a particular phone. Without probable cause or a warrant, the police, who suspected Smith of a crime, installed a pen register on Smith’s calls at his telephone company. The Supreme Court held that this was not a “search” for purposes of the Fourth Amendment, because people know that the phone company keeps records of their phone calls, “a person has no legitimate expectation of privacy in information he voluntarily turns over the third parties,” and Smith voluntarily “assumed the risk that the company would reveal to police the numbers he dialed.”
It is on the basis of this line of decisions that commentators have correctly stated that, under existing law, the government’s program of collecting phone-call data from phone companies does not violate the Fourth Amendment.
This is not to say, of course, that the Supreme Court decisions are “correct.” In his dissenting opinion in Miller, for example, Justice William J. Brennan, Jr. objected that an individual should be held to retain a “reasonable expectation of privacy” in the financial records he discloses to his bank, because such disclosures are “not entirely volitional in circumstances in which “it is impossible to participate in the economic life of contemporary society without maintaining a bank account” and because, in the course of his financial transactions with his bank, a depositor inevitably “reveals many aspects of his personal affairs, opinions, habits and associations.”
But even if Miller and Smith are correct in terms of the meaning of the Fourth Amendment, the mere fact that government can constitutionally exercise its authority in this manner does not mean that it should do so. That something is constitutionally permissible does not make it sound public policy.
http://www.thedailybeast.com/articles/2013/07/01/why-bush-violated-the-fourth-amendment-and-obama-has-not.htmlPlease note what the author (a law professor) says at the end. The Court may not have been right in these decisions; and even if it were, it doesn't necessarily mean that the government should proceed on this basis as a matter of policy, even if it has been deemed "constitutional."
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