"[B]y threatening to withhold Social Security checks from Americans, unless he gets permission by Aug. 2 to continue increasing the debt ceiling, President Obama is once again deploying a scare tactic strategy based on a falsehood," he added.

Obama said on CBS News that Social Security payments are at risk without a debt-ceiling agreement. But Gohmert said Social Security's ability to make payments on time in August would be "completely unaffected" by the status of the debt-ceiling talks. He said payments from the Social Security Trust Fund make payments possible for "many months."

"Unless the president and his Treasury secretary willfully withhold Social Security checks to make a political statement, seniors have nothing to worry about," he said. "Instead of being a statesman leader and saying something like, 'The only thing we have to fear is fear itself,' this president tries to create fear and panic in the American public at every turn."