In shutting down the government, most memos cite the law as the reason. The Government Accountability Office says employees who violate the Antideficiency Act may be subject to disciplinary action, suspension and even "fines, imprisonment, or both."

The law is the Antideficiency Act , passed by Congress in 1870 (and amended several times), which prohibits the government from incurring any monetary obligation for which the Congress has not appropriated funds.

Administration officials now live in fear of a 19th-century law that could get them fired, penalized or even imprisoned if they make the wrong choices while the government is shut down.

CNBC has learned that in several executive branch departments, high-level staff members review individual decisions about what government activities to allow for fear of running afoul of the Antideficiency Act. One White House official said he has advised his employees not to check their email or cellphones. Under the act, even volunteering for government service is expressly prohibited.

In a memo to his department employees today, Treasury Secretary Jack Lew cited the law as the reason for reduced staffing.

"For the duration of this impasse, as required by the Antideficiency Act and directed by OMB, the Department will be required to operate with only the minimal staffing level necessary to execute only certain legally exempted activities," Lew wrote.

The only exemptions to the shutdown concern "emergencies involving the safety of human life or the protection of property," according to government documents. That has meant airports and the Postal Service are open, Social Security checks get paid and federal prisons and courts will operate as normal as do most national security functions including the military and the Central Intelligence Agency. But national parks and museums are closed along with big parts of the departments of Education and Commerce

Congress passed the law as part of a struggle—dating back to the nation's founding—for control over the power of the purse. Some presidents, such as Abraham Lincoln during the Civil War, would incur obligations for which Congress had to appropriate funds after the fact.

What is ironic is that Congress in shutting down the government has to at least to some extent given up the power of the purse to the executive branch. Under the broad guidelines of what constitutes an emergency or threat to life or property, OMB now more or less decides what gets funded and what doesn't. But that latitude is limited by the fear of officials that, sometime after the event, a given decision is found to have been in violation of the Antideficiency Act.

—By CNBC's Steve Liesman. Follow him on Twitter: @steveliesman

