How badly will the shutdown affect my chances of getting a passport in time?

Fiance and I tentatively have plans to go to St. Lucia in May for our honeymoon.

Neither of us have passports (I had one but it expired over a decade ago). I still need to update my address at the DMV before I do any of that, but planning to do so ASAP. Goal is to have everything taken care of by the end of the month.