TexTaxToo is correct, and you are correct, Corduroy Frog.
You do have until the later date. But Drake won't allow scheduling payment after the *current* date if that date is after 4/15. The only way to pay later, electronically, is by doing so online via Direct Pay or EFTPS. Or, your client can mail a check to arrive by the date they want to pay. The IRS is very quick about cashing checks; it's about the only thing left that they handle expeditiously.