After more than a month of this political nonsense, the money has basically run out everywhere on the U.S. side and I would not expect any interviews to be taking place. There have been no official posts from CBP since December 21, since funding for their website evidently ran out, but Rep. John Lewis (D-GA) has a government shutdown FAQ last updated January 10 which notes that Global Entry applications are not being processed (even the online portion).
On the Canadian side, CBSA has posted a notice advising
Some of the NEXUS enrolment centres in Canada are open and are completing the Canadian portion of the enrolment process for clients that had appointments. Please contact the enrolment centre prior to attending your previously scheduled appointment.
When the United States government shutdown has ended, applicants will need to reschedule the interview with the U.S. Customs and Border Protection to finalize the process.
The Canadian Embassy sent an update today that CBSA will conduct a mobile NEXUS enrollment session in Washington, D.C. from February 5 to 7, replacing the January event which was canceled due to the shutdown.
Cross your fingers and hope that the budget impasse is resolved before your interview. If so, then you should have your interviews as scheduled; interviews scheduled during the lapse are simply cancelled, and are not rescheduled automatically.
CBP is funded through the appropriations process, unlike CIS, for example, which is self-funded through fees. Despite how distressingly frequent appropriations lapses have become, there is still uncertainty in a shutdown because different offices and employees may be designated as essential, and different programs may have been funded through separate vehicles. Living in the Washington area, I have many friends who are federal employees, and more than a few have been told to check the website on a daily basis to see whether they should sign in or not.
Unfortunately, this means that your best for accurate information about the interview will be to contact the interview center. In theory, because NEXUS is a cooperative program with Canadian officials, DHS officials might prioritize it over, say, GLobal Entry (which closed at least one office during the last shutdown), but that is just a hope. There were anecdotal reports of NEXUS interview cancellations posted to FlyerTalk last January.