Current Account Balance = Trade Balance + Net Income + Net Transfers = Savings - Investment. As trade balance is usually the largest part of the current account, a trade deficit is usually the current account deficit, which means savings is less than investment. The difference between the two, aka the deficit thus must bridged via foreign financing, of which 50% is done by the US Gov via IOUs such as treasuries. So there is a relation between the gov debt and overall debt, in the Twin Deficits Hypothesis.

US goverment is about to become much bigger, because of the goverment lowering govermental income (lower taxes + slashing tax collection and enforcement).