“It is not conceivable to me that all of this is not automated.”

Obama took office with the hope that these hang-ups could be separated from Washington’s endless wars over the size of government. In theory, these are problems everybody wants to fix.

“The question we ask today is not whether our government is too big or too small, but whether it works,” Obama said in his first inaugural address.

In many places, however, these federal systems still don’t work well. Some of the explanation can be found here, in this baroque underground bureaucracy.

During the past 30 years, administrations have spent more than $100 million trying to automate the old-fashioned process in the mine and make it run at the speed of computers.

They couldn’t.

So now the mine continues to run at the speed of human fingers and feet. That failure imposes costs on federal retirees, who have to wait months for their full benefit checks. And it has imposed costs on the taxpayer: The Obama administration has now made the mine run faster, but mainly by paying for more fingers and feet.

The staff working in the mine has increased by at least 200 people in the past five years. And the cost of processing each claim has increased from $82 to $108, as total spending on the retirement system reached $55.8 million.

In a statement issued Saturday, OPM Director Katherine Archuleta said: “I do not believe that the current level of service is acceptable.” She added that modernizing the system is a priority for her.

In an interview inside the mine this month, another federal official called the operation “very successful.”

But that official balked when asked if it was modern. “What does ‘modern’ mean?” the official said. The Office of Personnel Management allowed a reporter in the mine on the condition that interviews with some officials there would not be conducted on the record.