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> they are borrowing it

People have been saying that deficit spending will catch up to us since I was a kid, 30+ years ago. Every time deficit spending starts "catching up to us", the government responds with more deficit spending. It seems unsustainable to me, but there are people like Krugman who assure us that this can go on forever.

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If the economy grows by ~3% per year on average, and the interest rate is ~1% on government debt, can the debt actually "catch up"?

Depends how big a deficit you're running each year. But 'catch up' is a really vague term. As long as you can keep borrowing at low interest rates there's no problem, you can just borrow more to pay the interest, but eventually people will start to doubt your ability to pay it all back (yes this is irrelevant if a country exists forever, but infinity is weird like that).

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