The budget deficit is not the trade deficit. You are not taking on debt when you purchase a foreign good, just like you as an individual don't take on debt when you go to Walmart and exchange money for goods but Walmart doesn't buy anything from you.

The US domestic economy is vastly larger than its foreign trade (which is only 20% of America's GDP), so you can in fact run a persistent trade deficit and a budget surplus at the same time, which the US actually did for a while during the 90s and early 2000s. We need to teach more economics honestly.