If you look in the Constitution, you won't see the word "privacy" anywhere. You also won't see any reference to schools, libraries, and countless other things that are part of daily life. However, if you look at the 9th Amendment and the reason for it, it isn't hard to infer a right to privacy.

The 9th Amendment reads as follows:

Amendment IX - Construction of Constitution. Ratified 12/15/1791.



The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.



In essence, the 9th Amendment states that we have more rights than those specifically enumerated in the Constitution such as speech, religion, etc. The right to privacy would fall into that category. Furthermore, other amendments such as the 4th Amendment would imply a right to privacy. It reads:

Amendment IV - Search and seizure. Ratified 12/15/1791.



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.



As for Santorium's remarks, I think the operative point he's making is this:

And if the Supreme Court says that you have the right to consensual sex within your home, then you have the right to bigamy, you have the right to polygamy, you have the right to incest, you have the right to adultery. You have the right to anything.

Legally speaking, I think he's right. It all depends on the wording of the Supreme Court ruling. If it indeed says there is a right to "consentual sex within your home", then that implies any form of consentual sex is allowable. I doubt the ruling will be that broad, though.