I think the answer is: pay what I can on April 15, pay 20 percent over the rest of the year, and keep my eyes open for places to catch up, because I'll need to catch up at some point.
Are you a freelancer? If so, your third-quarter taxes are due on September 17. Are you freaking out? Do you have a big bill, but aren't sure where the money will come from? Do you have no real idea how much the payment should be?