It appears increasingly likely that Congress will fail to pass the 12 appropriations bills that fund various federal government agencies by the Sept. 30 deadline.

Failure to pass the bills would mean many government operations are halted and hundreds of thousands of federal employees are furloughed—including those at the Social Security Administration (SSA), which administers the Social Security system.

But while some Social Security operations might be affected by a shutdown, legal experts say Social Security recipients need not worry about one thing—their money.

"As a Metairie disability lawyer, every time a government shutdown is in the news, I get calls asking 'Is Social Security affected by a government shutdown?'" Louisiana-based attorney Loyd J. Burgeois said in a note on his website.

Mr. Burgeois said that staffing would be limited at SSA offices as many employees would be furloughed.

Some operations might be affected by a government shutdown—such as halts to processing of new Social Security claims, as happened during the 2013 shutdown.

"During the Clinton-era shutdown, new Social Security claims were not being processed because the agency furloughed 61,415 employees," Mr. Burgeois said. "As the shutdown wore on, the agency adjusted its plan and recalled workers to start processing new claims."

However, while some SSA operations would be impacted, Mr. Burgeois said Social Security checks will continue to be sent out.