...hits the correct answer on the profound difference between sovereign issuers of endogenous currency and those subject to liquidity risk (I disagree with the "borrow from the central bank" part, but that is a trifle)
U.S. debt is a problem, but not a crisis. If worse comes to worse, the Treasury (with the help of Congress) could prevail on the Federal Reserve to buy its debt at prices more favorable than those demanded by foreign creditors. If not sterilized, thus neutralizing the impact of the purchases on the money supply, the Fed would be monetizing the debt and a pickup in inflation would be the likely outcome. Indeed, that is what people mean when they refer to “inflating your way out of debt.”
A developing country that cannot issue debt in its own currency, but must issue it in another currency, say U.S. dollars, must earn the dollars necessary to service and redeem the debt through foreign trade (or perhaps temporarily through foreign borrowing to roll the debt over). It does not have the luxury of borrowing from its own central bank to service and redeem the debt.