Yes, it is possible to get a deposit on the weekend, depending on your bank. Tax Refunds are processed by the IRS two times per week. On the first day, the IRS only processes refunds that it will make through direct deposit, and on the second processing day, the IRS mails all refund checks to taxpayers who don't choose direct deposit. The IRS office hours of operation are Monday through Friday. See:
https://goo.gl/EdKGpq