Because listening in on my private conversations is a lot different from trying to find out if some convicted murderer wants a gun.
Warrantless searches are also prohibited by the Fourt Amendment. Background checks aren't. Nor has the second ever been interpreted in any way that says they are.
Ask him if he's bothered by the warrantless searches or by the denial of habeus corpus for the people in Gitmo. Somehow I think he won't be such a "strict constructionist" then.