The Constitution does not bear your opinion out. Judge Bork pointed that out during his Supreme Court appointment hearings and was torn apart for doing so, but he was right. Privacy is not listed as a right in the Constitution. How can you say that it is "as important" as the others you list? The others all show up. Privacy doesn't.
Jacquerie rightly attributes the interest of privacy to the fourth amendment...but be that as it may, I do not require the Constitution to define my rights. It was the understanding of the founders that the purpose of the Constitution was to limit the prerogatives of government, not enumerate the rights of the people. Indeed, many argued against their enumeration in the Bill of Rights specifically because it would appear to set the precedent that the rights of individuals were limited to what was specifically listed in the document.
I say no, emphatically no. Yes, there is a limit to rights...but my limit to this one is further than our current administration would have it placed.