Should I file my tax return by the due date even If I can't pay what I think I will owe?

Yes. There are different penalty and interest calculations incurred for not filing timely, not paying and not paying timely, or when a balance due exists. You will want to avoid the failure to file by the due date when a balance due exists penalty. Therefore, file the tax return by the due date and pay whatever you can at that point in time to minimize your total penalty and interest calculations.