Err...ignoring the debt ceiling? The debt ceiling is a legal limit. If the President instructs the Treasury to ignore the law, he can (and probably would) be impeached. As part of the article, the House would probably toss on a whole pile of added offenses, including the stimulus and bailouts, and the war in Libya, etcetera. It'd get ugly for the President, indeed.
The courts have no independent standing to decide anything, including the consitutionality of a debt ceiling. To weigh, an independent party with standing but bring suit. In the case of impeachment, the President would have standing to appeal the constitutionality of his impeachment, on the basis that the underlying law itself was unconstitutional.
To reverse the order, a party would have to show direct harm as a result of the presidents decision to break the law in order to sue. With the debt ceiling, this would be very difficult to do; the most likely candidate would be a group of lawmakers (whose authority has been circumscribed), but here the courts have historically been skeptical. Lawmakers are encouraged to manage their disputes internally using their existing constitutional powers, through legislative or impeachment means. It would probably take a majority of even supermajority of lawmakers to make "standing", and if such a majority exists, why not impeach rather than bring suit?
As an aside, there is not a chance in hell that the courts would agree with an interpretation of the 14th Amendment which authorizes the President to ignore congressional spending power (specifically, the 14th amendment says debt authorized in article 1, which gives congress the authority to borrow, shall not be questioned - it doesn't give the president the authority to issue new debt unilaterally). It won't matter, though; the Senate would almost certainly fail to follow the House in formally impeaching the president. The damage would be entirely political, but it would be severe. The president is much too politically aware to ever go this route.