Another problem with the analogy is that you can meaningfully make a $0.01 payment on your debt. You can pick any arbitrary percentage of your debt and pay it off right now, if you have the money to do so. Programming tasks are not only more (unpredictably) quantized than that, they're usually Sisyphean: if you do a little but don't finish, you've wasted the time you spent because the boulder rolls back down as soon as you stop pushing.
You can never make a $0.01 payment on any debt. You can try, but interest means your debt will grow faster than your payments! In the case of technical debt, interest is the recurring costs of working in the less than ideal code.