The shutdown - the first for 17 years - has left more than 700,000 employees on unpaid leave since 1 October and closed national parks, tourist sites, government websites, office buildings, and more.
The nation's 1.4 million active-duty uniformed military personnel remain on duty.
However, about half of the defence department's 800,000 civilian employees stopped work at the beginning of the shutdown - with the exception of those engaged in activities that "provide for the national security".
But on 5 October, the department said it would recall nearly all of these workers.
Defence Secretary Chuck Hagel said the decision was based on an interpretation of the Pay Our Military Act, which was passed by Congress shortly before the shutdown.
It permits employees "whose responsibilities contribute to the morale, well-being, capabilities and readiness of service members" to be exempted from the shutdown.
"I expect us to be able to significantly reduce - but not eliminate - civilian furloughs under this process," Mr Hagel said.
(only if shutdown continues)
The Department of Energy has said it can continue to operate for a short time without sending workers home. However, if the shutdown continues, plans are in place.
According to the plans, some facilities will have to close, with only 1,113 out of 13,814 staff required to work.
Exemptions include staff overseeing the safety of the nation's nuclear arsenal and operating dams and power lines across the country.
The National Nuclear Security Administration, which oversees the nation's nuclear weapons and naval reactor programmes, will have 343 employees on duty to "perform functions related to the safety of human life and the protection of property".
More than 400 employees will stay on to work at the Southwestern Power Administration and the Western Area Power Administration, which are in charge of overseeing hydroelectric power and power lines in the south and western US.
Some staff in other areas will remain at work to oversee "the protection of human life and property."
Most of the department's staff have been sent home. However, staff at the National Oceanic and Atmospheric Administration continue to report for duty to ensure weather, shipping and other reports are still provided for public safety.
Some of the workers at the Bureau of Industry and Security, which reviews exports, also remain on duty.
Transport roles run by the department, ranging from air traffic control to airport and hazardous materials inspections, continue and 36,987 out of 55,468 personnel remain at work.
Staff involved in overseeing commercial space launches also continue operations.
Suspended activities will include facility security inspections, routine personnel security background investigations and the employee drug testing program.
The National Zoo and 19 museums and galleries, including the Natural History Museum, the Portrait Gallery and the Air and Space Museum, are closed.
Of the 4,202 employees, 688 are being retained to "protect life and property" - security guards, maintenance staff and people to care for and feed the animals at the National Zoo.
The Smithsonian Institution says: "During a shutdown, the Institution cannot legally accept voluntary services from federal employees to continue their regular duties."
National parks - from Yosemite to Alcatraz and the Statue of Liberty - have been shut down with 3,266 essential staff out of 24,645 remaining on duty. These will include some fire management, law enforcement and emergency responders.
However, some states have asked the Obama administration to allow them to foot the bill for reopening their parks.
Governors say closures have impacted on local communities and businesses that rely on tourism to survive.
About 86% of the Department of Homeland Security's 240,000 employees are expected to be exempt from the shutdown, including uniformed agents and officers at the country's borders and ports of entry.
Most members of the Coast Guard, Transportation Security Administration, Secret Service and other law enforcement agencies are also exempt.
US Citizenship and Immigration Services employees will continue to process green card applications.
Of 114,486 Department of Justice employees, an estimated 96,744 are exempt from the shutdown.
All Federal Bureau of Investigation (FBI) agents and support personnel in the field are exempt as their operations are focused on national security and investigations involving protection of life and property.
Drug Enforcement Administration agents working on active counternarcotics investigations, agents in the Bureau of Alcohol, Tobacco, Firearms and Explosives, and US attorneys are also still at work.
Staff at federal prisons are also working.
The department has sent home more than half its workers.
The Centers for Disease Control and Prevention will continue "minimal support to protect the health and well-being of US citizens".  However, fewer staff will mean reduced capacity to respond to outbreaks and the agency will be unable to support its annual flu program.
Nearly a dozen experts on foodborne illnesses were called back to work in recent days, partly to help with a salmonella outbreak.
About 212 of the department's 4,225 employees - both full and part-time - were expected to work for the first week of shutdown. Initial plans stated an additional 30 staff would be called in if the shutdown lasted more than seven days.
Some $22bn of funding to schools, due on the 1 October, was to be distributed. Among other things, this pays to help educate poor and disabled children.
Administrator Gina McCarthy said her department would effectively shut down with only a core group of individuals available in case of a "significant emergency".
The self-funded  US Postal Service remains open and is delivering as usual. The agency receives no tax dollars for day-to-day operations and relies on income from stamps and other postal fees to keep running.
The US government remains in partial shutdown after negotiations between Republicans and Democrats failed to find a solution to an ongoing dispute over the federal budget.