Get this straight, the US has "sovereign debt", not "sovereign currency". Since we do not have monetary sovereignty, we have to "borrow" Federal Reserve notes (AKA Dollars) into existence, with interest, from the Federal Reserve. The Government borrows dollars by issuing Government bonds, bonds that carry a interest rate obligation.
Every dollar in circulation then represents a debt to be payed back, with interest. The Government needs to "create" more dollars to pay back the interest on the dollars it just borrowed. And how are these new dollars created?
Government can't print them, gave up that right a hundred years ago... but it can trade interest-laden bonds for them. They could also get them from the existing dollars in public circulation by perpetually hiking up tax rates, but that just leads to political turmoil. So they are created quietly by borrowing more dollars from the Fed, through bond issuing, each new dollar with its respective interest rate attached... which needs to be payed with yet more new dollars, which also have their own interest rates attached.. You need perpetual, exponential growth to cover that sort of loan deal.
How can a country get out of debt when the currency it is forced to use is based on debt?