This is probably a crazy, stupid idea for getting around the debt ceiling, but...

...here goes anyway. 

Consider a 30-year Treasury Bond with a coupon of 4 percent and a par value of $100.  Treasuries pay every six months, so this produces 60 cash flows of $2 and then $100 at the end of the 30 years.

To make things easy, assume for a minute that that market is discounting 30-year bonds at 4 percent per year (or 2 percent per six months).  Suppose the US government offers investors a swap of 4 percent coupon bonds for 8 percent coupon bonds.  If we don't worry about duration issues for a moment, and use Excel notation (I don't know how to get Greek symbols in blogger), investors would be indifferent between:

PV(.02,60,2)+100/(1.02^60)

and

PV(.02,60,4X)+100X/(1.02^60).

X is the face value of the new bond, and comes out to about $58.99.  So the face value of the debt is reduced by 41 percent, while the value to investors remains constant.  Nothing of substance has changed (and actually duration risk is a little lower), but the balance sheet looks better.

I am sure I am missing some institutional thing here, or maybe my simple finance is off somehow, but still...