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I have been paid by the government for more years than I want to count. Between military, DOA, and the VA I can say with 100% certainty that I have NEVER been paid on a weekend. Generally I would get paid prior to the weekend or holiday or in few cases, just after. I would wait until Monday before freaking out.
You should have received the deposit on 12/31/15. With Social Security payments when your payment date is on a weekend or holiday during the week the payment is deposited the previous business banking day. Since SSI pays typically on the 1st and regular SS benes on the 3rd everyone should have received their funds on Thursday.