According to the Huffington Post, the Debt Limit will be reached on December 31, 2012. Treasury Secretary Timothy Geithner will take measures that will postdate the date, but as the article mentions, the uncertainty about the fiscal slope, namely taxes and the sequester make it very difficult to know how long he can put the debt ceiling off.
In a letter to Senate Majority Leader Harry Reid (D-Nev.), Geithner said that the measures would add about two months -- or an additional $200 billion -- to the limit under normal circumstances. However, given the tax and spending uncertainty due to the so-called fiscal cliff, Geithner said, he cannot predict how much time the measures will actually allow.
Given that we have already seen extreme dysfunction when the House couldn't even pass "Plan B" which was a completely Republican bill, I am slightly pessimistic about our chances of escaping the slope and the debt ceiling without the United States going into an austerity-caused recession or Democrats being damaged by concessions on earned benefits that may be necessary to save this country from plunging the world into a global depression. At least that it seems that Democrats will be the ones that have to pass anything dealing with the slope and the debt ceiling because the GOP is wholly incapable of governing and ought to be thrown out of Congress for dereliction of duty.