According to the USCIS website, very little, at least initially. Since USCIS requires fees for almost all services, they will keep operating.
They are reminding everyone to attend all appointments and interviews as scheduled.
The EB-5 program will continue to operate but not the centers and certain applications will not be processed until further notice such as the I-924s. (link here)
E-verify won’t be available during the shut down.
We will update any information we have as more details become available.