Is the apt. actually a subsidized one? Because I would think that a person who owes money would qualify for something like that, vs someone with enough money to pay for everything up front. Or did you just fritter that money :-). Without knowing a lot more about where you live (with regard to local regulations, etc.) or the nature of the 'low income' program, etc., it's hard to guess.

Most apartments look at your credit score and debt to income. In other words even with the debt you might have great credit. And you income might be enough to make your minimum monthly payments, rent, and have extra money.

I'd try to start by getting a credit report with a score on it.