I don’t think Obama has the authority to hold up the SS checks. They are not attached to the debt ceiling. Currently the SS fund has billions in surplus. Enough to keep paying SS for months.
Obama can pay or not pay almost anything he wants. The law just says the SS Administration has to send the information about what is to be paid to whom that month to Treasury Dept. on time. It doesn’t mandate that Treasury Dept. send out the checks.
Oh BTW there is no SS fund except on paper. All SS payments are from current income.