if you use the USPS you probably should use a tracking method so you know the IRS/state got the payment. The USPS has been known to lose mail. that includes tax payments and returns. then you are on the hook for late filing/payment penalties and interest. you can pay the IRS electronically through its website and your state, if you have a state income tax, probably can be paid electronically as well.
those websites allow you to specify the date the money is to come out and you can print a receipt with tracking info should there be an issue. I never have had one and the money always comes out on the timely date I specified (not Saturday or Sunday).
https://www.irs.gov/payments
