A mess is definitely a technical debt. It's going to take time and money to clean it up. You can put it off more, but it's going to make everything cost more money and take more time than it should. Or you can clean it up now and save that time and money.
Debt is one way that companies get ahead when they are first starting out. Just like borrowing money, you can borrow time from the future as well. Instead of making an immaculate product, you make something that gets the job done and fix or rewrite it later.
And just like money debt, if you don't pay off your technical debt, it will be a real pain. And the longer you wait, the more expensive it is.
Seriously, the analogy is crazy good.