The Republicans have deliberately exaggerated the importance of the public debt.
Debt Held by the Public Intragovernmental Holdings Total Public Debt Outstanding
02/07/2014 12,280,064,393,437.44 4,978,760,297,100.09 17,258,824,690,537.53
http://www.treasurydirect.gov/NP/debt/current
As you can see, the $12,280 trillion debt held by the US public can only be paid by raising taxes, and the Republican house won't do it.
Leaving the intragovernmental Holdings (foreign debt) $4,978 trillion, the only debt to be seriously concerned with.