Predicting these things is impossible. The question is not the average time for a passport, but whether there is an issue with your passport documents or any of the information in the documents. The 2-3 weeks is not unreasonable, but any small issue can result in the entire package being returned to you.

The good news is that when you get down to 2 weeks to go, you may deal directly with a Passport Agency and there is one in Hot Springs. While this means a day out of your life (actually head out the night before so that you are there before opening time). Chances are that you will wait around and have your passport a few hours later. At worst, the passport will be overnighted to you.

Pay close attention to the required documents and have everything proofread by someone else because everything will have to be redone if there is a mistake.

Have paper printouts of your e-ticket receipts as proof of travel and, if things get really tight, just show up at the Passport office without an appointment.

https://travel.state.gov/content/pas.../arkansas.html