General operations interrupted. National parks would close, as would District of Columbia tourist sites such as museums on the National Mall. But the definition of "essential" can be subjective. In a 1995 shutdown, hot line calls to the National Institutes of Health concerning diseases weren't answered. Air traffic controllers were essential, but the State Department stopped processing visa and passport applications.
Social Security. Social Security checks would continue to be paid, but new enrollees might be delayed starting their benefits.
Medicare. In the 1995 shutdown, seniors' Medicare payments flowed as usual. Doctors and hospitals are expecting the same would occur this time.
Postal service. Mail delivery and post office operations should continue as usual, because the postal service operates with its own funding stream from those "forever" stamps and other postage fees.
Taxes. Americans will still need to file their taxes on time (April 18). The Internal Revenue Service has said it will process electronic returns, but its processing of paper returns would be delayed by a shutdown. Will electronic filers get refunds promptly? They may soon find out.