Actually my statement doesn't depend on exponential growth. If in future GDP were to switch from exponential to logarithmic growth, debt would still be serviceable as long as it also switched to logarithmic growth.

Come on, that's silly. At some point, for all intents and purposes in the real world, logarithmic growth would essentially mean "no growth". Splitting hairs between the continuous math and the math to a reasonable level of precision doesn't add clarity to your statement.

OK maybe over hundreds of years US GDP will go from exponential growth to linear growth, to logarithmic growth, to eventually "no growth". If total debt mirrors this trajectory, can't the US government continue repaying its debts over this period, even at the "no growth" stage?

Infinite != indefinite :)