Yes, today is the due date for payments, and an extension does not change that.
Penalties for your personal tax return are based on the amount that you owe. If you do not owe anything (such as getting a refund), there is no penalty. So yes, it is a good idea to make your payment in full (or more than you think you will owe) today if possible.
IRS Direct Pay is the easiest way to do so.
https://www.irs.gov/payments
