how lenient are courts with payment extentions on a D.U.I ?

Answer 1

This will vary by judge. If you honestly state what you can do, and lay your financial status open before the judge, and don't have a reputation for ignoring the courts, they will probably let you set the terms.

But they might let you sit in jail for a time instead of a fine.

Answer 2

The courts have a lot of discretion in this area. Talk to the judge, agree on a payment schedule, and stick to it. You should be fine.