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todays Treasury Statement (May 16 statement date) here is the breakdown on the total debt limit and total debt outstanding.
the total public debt outstanding is $14.345 trillion. Thats approximately $52 bln over the limit.

This shows the debt ceiling is meaningless. It also shows that the government can keep on spending and issuing debt and if it does, the Republicans lose all the leverage that they think they have on spending cuts and debt reduction.
The question is, does Obama and Geithner know this?