As Posner indicates, the US is facing an immediate debt problem, a medium term deficit problem, and long-term debt and deficit problems. We have discussed several times the long-term fiscal problems (see, for example, my discussions on 11/07/10 and 7/17/11), so I will concentrate here on the shorter-term deficit-debt issues.
With the sole exception of the mid-1990s, the federal debt ceiling has always been raised on time during the past 60 years to accommodate the growing level of the debt. Although little time remains to raise the ceiling I do not believe either party will risk the political fallout from not adjusting the ceiling before the government effectively defaults on its obligations. Certainly Republicans remember the political cost to them after the Gingrich-inspired shutdown of the federal government in 1995. So I would be quite surprised if a deal is not reached this time before the US government is forced to delay payment on some of its implicit obligations, such as Medicaid and Medicare payments.
Of course, an absolute ceiling on the debt that is just raised continually makes little economic sense. the relevant size of government is not measured by the absolute level of its debt since large economies tend to have much more debt than do small economies.
etter metrics of the debt burden would be the ratio of debt to GDP, or the ratio of interest payments on the debt to GDP, or perhaps the share of interest payments in total government spending.