This is far more problematic than markets realize.
The president had a choice. The debt ceiling thing expresses 'the will of Congress' where Congress makes laws for the executive branch to execute.
The president has also sworn to uphold the Constitution which says the president has to pay the nation's bills. The President has so far decided to abide by the will of Congress.
The called for Sequestration Solution
And, in any case, the Republican leadership says the fight is going to be about modifying the already in place sequestrations. So seems it's now 'advantage Republicans' on the spending cuts issue.
And the Resulting Problem
The economy hitting the debt ceiling and going cold turkey to a balanced budget is a far more catastrophic event than even going over the full cliff would have been, as it disables the 'automatic fiscal stabilizers' and instead triggers a pro cyclical downward spiral in output and employment.
That is, when the $25 billion/week spending cuts kick in and the economy slows, the falling tax revenues mean spending has to be cut more, nor can total spending on unemployment 'automatically' go up, etc.
And don't forget about the Jan. 1 highly regressive FICA hike now beginning to kick in which also seems markets are not discounting.