Now that the U.S. debt limit has been reached again depite being raised by $2.1 trillion (to $16.4 trillion) less than 1½ years ago, the limit and possible ways for Obama to evade it if House Republicans refuse to raise it have been debated, so I will offer some thoughts on the issue here.
On the one hand, I sort of agree with those liberal critics who argue that it makes no sense for Congress to on the hand make certain taxation and spending decisions and then to make a decision about debt unrelated to that. Since the change in debt is an arithmetic result of the difference between spending and revenue, making two decisions could be seen as a denial of the laws of arithmetic.
However, this doesn't necessarily mean that the debt limit is illegitimate, it could just as well imply that the decisions authorizing unlimited deficit spending are illegitimate. After all, most people have actual or potential debt limits in terms of how much creditors are willing to lend them. This means that one has to try to increase one's incomes or reduce spending once one comes near the limit. Regardless of whether one thinks that would be a good policy for the government or not, it is certainly consistent with the laws of arithmetic to adjust revenue and spending policies instead of doing away with the debt limit.
And as it happens, the debt limit represents the best chance of achieving what the talks of the "fiscal cliff" utterly failed to achieve (indeed, they in fact quite to the contrary resulted in higher spending): namely lower spending in exchange for a higher debt limit. That was in fact what happened at the latest drama over the debt limit in 2011, though none of the cuts have actually been implemented yet.
However, "best chanse" doesn't mean it will actually happen. Obama and the Senate Democrats have in fact several options to prevent spending cuts. One is to simply refuse to negotiate, which is the current White House official policy, and hope that Republicans, out of fear of being blamed for the negative consequences, will simply surrender once all established tricks to evade the debt limit has run out, This will however most likely not work.
There are two ways of evading the limit that have been widely dsicussed. One is to envoke the 14th amendment to the U.S. Constitution, that says “the validity of the public debt of the United States, authorized by law… shall not be questioned.”. It is doubtful that this can really be used to ignore the debt limit. After all, tax revenues are more than enough to pay for interest oayments so there is no need to default on debt payments even if the ceiling isn't raised. To use this amendment in this context one would have to consider Social Security and Medicare payments, and other decided upon spending, as "debt", and that seems like a long shot in legal terms. And for the moment at least, Obama seems to have decided against invoking this amendment with his spokesman Jay Carney clearly stating "This administration does not believe that the 14th Amendment gives the president the power to ignore the debt ceiling–period,"
Another way of evading the debt limit that have been proposed is to mint a (or several) trillion dollar coin(s), Mostly, only the Federal Reserve has the legal power to create money out of "thin air", and although the Fed is essentially a government agency it isn't so formally, meaning that it's money printing can't be used to evade the debt limit.
However, for some unexplained reason, the U.S. Constitution has left a loophole, allowing the U.S. Treasury to mint platinum coins of whatever denomination it likes. This could indeed be used by the Obama administration to finance spending even if the debt limit isn't raised. This option has recently been endorsed by several leading liberal pundits, including Matthew Yglesias and Paul Krugman. Though the Treasury's ability to mint platinum coins clearly wasn't created for this purpose, nothing, as I understand it, in the law actually forbids it from being used that way, and the law says it can be denominated in any denomination, this seems like a more realistic option for Obama than invoking the 14th amendment. Whether Obama will actually do it remains to be seen however. Though Yglesias, Krugman and many other leading liberals support it, Obama might view this option as too unorthodox.
In conclusion, it remains to be seen how useful the debt limit will be. If Obama thinks "the platinum coin option" is too unorthodox to , he will be forced to agree to spending cuts, which would be good. If however he fears spending cuts, not to mention being considered a weakling and a pushover by his fellow Democrats more, then it could instead simply mean a new powergrab by the President