That's actually not true. You can take out private educaiton loans from a handful of lenders that do not require school certification (Chase Education One loans come to mind, but there was a list floating around on here a little while ago with more of them) and do not use 'cost of attendance minus financial aid received' to cap how much you can get. they have a maximum amount, yes, but i think Chase's was 40K.
Let's not forget that there is a direct relationship between having a lot of consumer debt and defaulting on debt payments. If the OP tries to go to law school with 20K in consumer debt still hanging over his head, HE RUNS A VERY HIGH RISK OF DEFAULTING ON HIS PAYMENTS because they are going to be in the hundreds of dollars a month, during a time that he will already have a low income and be living on a tight budget. THIS is the main reason that it would be irresponsible of the OP to go to law school before addressing his debt.
My issue is that law schools are up front about needing to minimize debt before starting school, yet people on here are asking what to do a mere month before school starts. There are plenty of options available to people who have consumer debt such as going part-time and/or choosing a lower-ranked school to get a better scholarship. The OP has chosen to go to one of the most expensive schools in the nation in terms of tuition/COL when there are other closely ranked schools that are in cheaper areas that would have made making the minimum payments more manageable.
I have a lot of credit card debt too. I've been out of school for a long time, making very little money doing a non-profit job... it adds up. It's hard for me to understand where all this harsh judgement comes from? Life is messy sometimes. We mess up. Big deal. I think I can still make the minimum payments in law school. That's what I'm going to do. And then I'll pay it off eventually. My advice-- make sure you can get it all at a low enough interest rate that you can make the minimum payments through school. You'll pay it off when you get out.