I believe that interest paid on the "debt held by the public" is on budget. However, you are correct that all of the interest paid on the debt held by Social Security and the other trust funds is off budget. In effect, the government pays the trust funds interest but immediately borrows it all back off budget. Pretty slick, huh?
By the way, there was an incorrect statement in my prior post. The gross federal debt is projected to rise to $16.7 trillion (not nearly $20 trillion), increasing from the current 64.7% of GDP to 77.4% (not 91.5%) of GDP. Still, 77.4% of GDP will put the gross federal debt at its highest level since 1951.
They might still explain why, during periods in the mid 90s when both Congress and the Clinton administration were claiming we had a surplus, the debt kept increasing every month, every day, according to the Treasury.
I thought it was because debt service was off-budget. (I haven’t been able to find a line item in the budget for that.)