The Executive (President) will continue unheeded, until heeded. That's the nature of the office and the very reason we have a system of checks and balances to protect us from the occasional rogue Executive.
For 40 years, I’ve heard Watergate called a “Constitutional crisis”; perhaps it was, albeit a minor one. However, the Constitution worked, pretty efficiently and just the way it was designed. Heads rolled, the Executive voluntarily removed himself at the behest of congressional leaders from his party and White House conspirators were imprisoned.
In 2013, we have an Executive not only flouting the Constitution, but acting in absolute contempt thereof with complete support of his party and, apparently, the at-large press.
From my own layman’s view, this is “Constitutional Crisis” writ large.