The official [government website][1], found with a Google search for "passport services government shutdown", says, as of now: 

> You can still apply for a U.S. passport book or passport card at all
> passport agencies and centers and acceptance facilities (such as U.S.
> post offices, libraries, or county clerk’s offices) during the lapse
> of appropriations. You can also renew your passport by mail. Our
> processing times remain the same: 4-6 weeks for routine service and
> 2-3 weeks for expedited service.

Of course that may change.


  [1]: https://travel.state.gov/content/travel/en/traveladvisories/ea/passport-services-government-shutdown.html