Pay as much as you can toward the amount due, as soon as you can.
Certainly, make a partial payment by the 30th, if that's the best you can do. Make further payments when you can, before they bill you, if possible.
They are NOT looking to hang you, or garnish your wages. Yes, you'll have to pay some penalties and interest; that can't be helped.
Keep careful records of your payments.
The state tax department would much rather work out a payment plan than take you to court. Call them and talk about it. Communication will keep you out of trouble.