He went on to add: "The second situation is one where this standoff last several months, or several weeks. In that case it's probably safe to say that this would cause severe damage to the U.S. economy and the world."
U.S. debt securities are traded and held as safe investments throughout the global financial system and many officials and market participants say a failure to pay when they come due would cause serious disruption.
In his speech, Draghi said the eurozone economy will stay "subdued and uneven" for a while and emphasized that the bank has room to cut interest rates further to help growth.
Analysts say Draghi wants markets to know that the bank is nowhere near withdrawing its stimulus efforts, unlike the U.S. Federal Reserve. The Fed's discussion of ending its bond-purchase stimulus has unsettled markets around the globe.
The economy in the 17 European Union member countries that use the euro as their currency grew 0.3 percent in the second quarter, beginning a modest recovery after six straight quarters of decline.
The ECB has kept its benchmark rate at a record low of 0.5 percent, despite high unemployment.
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McHugh contributed from Frankfurt.