Why not a privacy amendment?

Dan Savage's Op-Ed today (reg.req.) asks a reasonable question:

If the Republicans can propose a constitutional amendment banning gay marriage, why can't the Democrats propose a right to privacy amendment? Making this implicit right explicit would forever end the debate about whether there is a right to privacy. And the debate over the bill would force Republicans who opposed it to explain why they don't think Americans deserve a right to privacy - which would alienate not only moderates, but also those libertarian, small-government conservatives who survive only in isolated pockets on the Eastern Seaboard and the American West.

Thanks to Angela Riccetti for this one.