There are rare cases in which a newly naturalized citizen may need to get an American passport almost immediately after taking oath (some countries may punish you if you take US citizenship and then use their passport, so make sure that you check the dual citizenship rules of your native country, and also it is illegal to try to enter the USA with another country's passport once you have naturalized -- you will be caught at the airport because the database is updated once you take the oath of citizenship). While you can apply for a passport immediately after taking the oath (research beforehand the nearest post office to the place of naturalization ceremony and show up with all the paperwork already completed so that all you need to do is to attach your naturalization certificate, which should be photocopied for your own record just in case something goes wrong), and if you use the expedite service, the passport should arrive in a matter of days, but if you need to travel in two weeks or need to apply for a visa within next four weeks, then you can apply in person at a passport agency by making an appointment.
But can a permanent resident legally make an appointment with a US passport agency while still awaiting the oath? Would it not be violation of the law that you are falsely claiming to be a US citizen? It might appear that way because only citizens are supposed to interact with the passport agency, but merely making an appointment is not counted as claiming to be a US citizen if you have already been approved at the interview for oath ceremony. Obviously, if something goes wrong and you are not able to take the oath, you will be wasting your time and money by visiting the passport agency anyway. On the other hand, if everything proceeds smoothly, when you do show up for your appointment at the passport office you will have all the paperwork needed along with your naturalization certificate. So go right ahead and make an appointment without worrying about anything.