Mark this down to the law of unintended consequences. It's possible – perhaps even likely – that Congress has already, inadvertantly, repealed the debt ceiling.
The current debt ceiling was signed into law on February 10, 2010, and that law sets a maximum amount of $14.294 trillion for the US debt. However, since that time, the 111th Congress (the last congress, before the 2010 elections) also passed various appropriation bills for FY2011 which are now in effect. Those appropriations legally authorize the government to spend money.
So we have one law that says to the government: you cannot spend money, and another law that says to the government: you can spend money. Now here's the question: when two laws disagree, which law takes precedence?
And the answer is: the most recently passed legislation is controlling.
And that would be appropriations. In effect, by passing appropriations whose authorized spending exceeds the debt limit, Congress may have already made a de facto repeal of the debt ceiling up to the authorized level of appropriations.
It's been speculated in various places that Obama could get around the debt ceiling by invoking the 14th Amendment, or by other means such as coin sovereignage. But it seems to me that a much simpler answer is at hand. All Obama needs to do is issue an Executive Order for the Treasury to issue more debt in order to meet currently authorized appropriations, under the theory that the authorized spending, being more recently passed, trumps the older debt ceiling law. While Article I of the Constitution specifies that only Congress can borrow money, there is no obvious reason why Obama can't invoke the appropriations bills as a valid Congressional authority to incur debt.
Of course, it would always be possible for Congress to "clarify" the situation, and re-authorize the current debt ceiling. In fact, Congress would never get the votes to pass such legislation, and obviously could never override a certain veto. And, even if they could (and did) re-authorize the debt ceiling after it has already been surpassed, and override a veto, then that law would certainly be unconstitutional under the 14th Amendment.
So by invoking this interpretation of the law, Obama can put Congress in a box of its own making, take the credit for avoiding a financial meltdown, and place the blame for increasing the debt where it really lies: on Congressional appropriations. And he can do so without a Constitutional showdown. It's win-win-win for Obama.