To look at a similar case, whereby somebody was using a phone to make illegal activities and the issue of the 4th amendment came up, I present this case:


Charles Katz was convicted in California of illegal gambling. He had used a public pay phone booth in Los Angeles to place bets in Miami and Boston. Unbeknownst to him, the FBI had attached an electronic eavesdropping device to the phone which recorded the conversation. Katz was convicted based on recordings of his end of the conversations. He challenged his conviction, arguing that the recordings could not be used as evidence against him.

Holding
So long as an individual can justifiably expect that his conversation would remain private, his/her conversation is protected from "unreasonable search and seizure" by the Fourth Amendment.
The Fourth Amendment protects people, not just places. Therefore, the rights of an individual can be violated, regardless of whether or not there is physical intrusion into any given area.
A warrant is required before the government can execute a wiretap, and the warrant must be sufficiently limited in scope and duration.

Decision and rationale
In the decision the Supreme Court sided with Katz, holding that the Fourth Amendment protect his right to privacy, wherever he may be. Justice Stewart wrote, "wherever a man may be, he is entitled to know that he will remain free from unreasonable searches and seizures. No less than an individual in a business office, in a friend's apartment, or in a taxicab, a person in a telephone booth may rely upon the protection of the Fourth Amendment." The thrust of the Court's argument was that the Amendment protects people and not just places. This ruling also extended the protection of the Fourth Amendment to include private conversation in addition to coporal objects.

"The Government's activities in electronically listening to and recording the petitioner's words violate the privacy upon which he justifiably relied while using the telephone booth and thus constituted a "search and seizure" within the meaning of the Fourth Amendment."

Justice Harlan's concurrence
In his concurrence, Justice Harlan noted that precedence has established two requirements for a person to justifiably rely that his conversation is private: (1) the individual must "have exhibited an actual (subjective) expectation of privacy," and (2) society must be prepared to recognize that this expectation is (objectively) reasonable. To Harlan the fact that the booth was enclosed was vital to the decision.

"It [the telephone booth] is a temporarily private place"
http://en.wikipedia.org/wiki/Katz_v._United_States


The question you injected Sarge, has no place in this issue. It's a question which YOU created, which has no origin in our laws or in our courtroom. It's what YOU would like the question to be, not what it ACTUALLY is...
The question is not whether or not whether or not their phone conversation could "not be possibly tapped".

The question is whether or not the U.S. citizen could have a reasonable expectation to privacy. And if there is a reasonable expectation to privacy, then a WARRANT is required...

And if you have a "SECRET" program to monitor phone conversations, which the public is not informed of, then how in the
h-e-double_hockey_stick can a citizen "expect" that his conversation could not be private with no warrant?