"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."
A plain English interpretation would seem to make the NSA slurping illegal, but a legal interpretation could be completely different.
(1) 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 (2) 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.
(1) being the protection, and (2) mentioning the loophole of warrants and protections on that as well. Searching digital information without a warrant violates (1). The legal way to do it is via warrants, and limitations on warrants are prescribed in (2).