The US national debt is 61k per citizen, 167k per taxpayer. Hopefully those numbers are more relatable. The government is racking up a credit card on our behalf, and our descendants will get the bill. http://www.usdebtclock.org/
Debt to assets or net worth might of the country be a more intuitive way to look at this, which would naturally include companies and corporations, which definitely should be included for a number like that. Unless the goal of the number is to incite fear and outrage instead of illustrate and educate. But who would do something like that?
The goal was to but a big number in a relatable context. If we're looking for a more fair ratio, that would be debt over GDP. That said, companies and corporations are ultimately owned by (mostly) citizens, so ultimately it comes back to a debt to personal income ratio.