All mainstream economists would gasp at the statement above, yet it is true.
A fundamental macroeconomic accounting identity is:
|i = s|
Which basically says that for every investor there is a saver. (We can also state it as follows: for every borrower their is a saver.)
In order for someone to "net save" someone else has to net spend or invest by the same amount.
Thus, if the United States Government is the largest debtor (we can say, investor, same thing), then the non-Federal-government sector of the U.S. and the rest of the world (ROW) are net savers.
If you don't believe it, just look at the graph below:
The graph shows that as the Federal deficit increased (gross savings of the Federal Gov't decrease), then the savings of the U.S. domestic sector (including states and localities) and the rest of the world (ROW) saw an increase in their gross savings.
I used a starting point of 1997 but the starting point is irrelevant.
Notice, too, that each time the gross savings of the government increased, the gross savings of the private sector decreased and vice-versa. In fact, the periods of rapidly declining government "savings" equated to periods of equally rapidly rising periods of private sector savings.
Lesson here is: Deficits add to private sector savings.