Trump's assertion, which his campaign manager insisted was irreversible, came less than one week before the kickoff Iowa caucuses. He once again defied the conventional rules of politics, and used his power and prominence to shape the campaign agenda and conversation.

So far, Trump's untraditional moves have only expanded his support, but his threatened boycott leaves him open to criticism that for all his tough talk he is ducking face-to-face confrontations with his opponents and scrutiny from the Fox moderators.

Given Trump's past flirtations with boycotting Fox, many will doubt his declaration until they see the other candidates take the debate stage on Thursday night without him.

The Republican debates have become must-see television, in part because of the allure of Trump's star power and unpredictable candidacy. But he said Tuesday that he thinks Fox and other television networks have been taking advantage of him by selling advertisements for their debates at a high premium.