The State Department would continue processing foreign applications for visas and U.S. applications for passports, since fees are collected to finance those services. Embassies and consulates overseas would continue to provide services to American citizens.
Social Security and Medicare benefits would keep coming, but there could be delays in processing new disability applications. Unemployment benefits would still go out.
Federal courts would continue operating normally for about 10 business days after the start of a shutdown, roughly until the middle of October. If the shutdown continues, the judiciary would have to begin furloughs of employees whose work is not considered essential. But cases would continue to be heard.
Deliveries would continue as usual because the U.S. Postal Service receives no tax dollars for day-to-day operations. It relies on income from stamps and other postal fees to keep running.
All national parks would be closed, as would the Smithsonian museums, including the National Zoo in Washington. Visitors using overnight campgrounds or other park facilities would be given 48 hours to make alternate arrangements and leave the park. Among the visitor centers that would be closed: the Statue of Liberty and Ellis Island in New York, Independence Hall in Philadelphia, Alcatraz Island near San Francisco and the Washington Monument.
New patients would not be accepted into clinical research at the National Institutes of Health, but current patients would continue to receive care. Medical research at the NIH would be disrupted and some studies would be delayed. The Centers for Disease Control and Prevention would be severely limited in spotting or investigating disease outbreaks, from flu to that mysterious MERS virus from the Middle East.