Per Rush Limbaugh, entitlements (includes SS) are not impacted by the debt ceiling.
So, this appears to be an outright lie.
IIRC, they used a similar warning/threat a few months ago when they were talking government shutdown — to which the SSA responded that checks would go out as scheduled, and that automatic deposits would also go out on time.
SS is in the red now. It is a pay as you go program. The General Fund must come up with the money to make up the shortfall, i.e., provide the funds to redeem the IOUs in the SSTF. Right now, Obama is assigning the priorities on what will and will not be paid as the revenue comes in.