Strict Construction v. Inherent Powers

Conservatives' ultimate goal for the judiciary branch of the government is a bench full of strict constructionists. Conservatives loudly decry judges who peer into the Constitution and find new rights, laws, etc.

We now know that the Bush administration -- which lays claim to the title of conservative, though many honest cons that I know either shudder or chuckle at the notion -- has been spying on U.S. citizens at home in apparent contravention of publicly-known law.

How are they able to do this? At least in part because, according to Attorney General Alberto Gonzalez, the president has "inherent authority under the Constitution" to institute the program.

Does anyone else see any tension between decrying jurists who find new powers/rights/etc in the Constitution and chief executives (or their lawyers) who do so?

UPDATE: "TypicalLiberal" in the comments section implies a double-standard on my part for not blasting the Clinton administration for having apparently (I have not seen the news reports but will take TL at his/her word) done the same thing. TL is using a typical DC debate strategy, which is to shift to reframe the debate. To wit, TL is trying to move the debate from one of conservative intellectual consistency (strict constructionist v. inherent powers) to Schlesinger consistency (criticizing Bush but not Clinton). So to answer the criticism, and knock out the GOP talking point, I do not cirticize the Clinton admin here because they made no claims to being "strict constructionists" and are thus not open (here) to accusations of hypocrisy.