Is it feasible to find rental home 2 wks before movein date?

I am moving from Pennsylvania to Murfreesboro, Tennessee. My current rent contract ends June 18, so I'm really hoping to be able to move in to a rental home June 19 or 20 if possible. However, with my work schedule, the only possible opportunity I will have to visit the area in person and see homes is May 28 through June 3. I realize this is really cutting it close, as I've been reading that general rule of thumb is to start looking 30-45 days in advance. I have asked my current landlord to extend by 1 week, but not sure yet if this will be possible. I would like to use a realtor, my hope being that this will expedite process of finding a home within that 1 week opportunity (I'm sure I would end up wasting a lot of time trying to do it myself through Zillow or something). So my question really is, is this timeline feasible or am I setting myself up for failure by trying to make this work? I have a pretty good idea of what I'm looking for, Zillow suggests there are plenty of options that fit the bill in the area - if there was a suitable place found in that week I am visiting Tennessee, can the rest of the process of finalizing the contract be completed in the remaining 2 weeks? Anything you could share would be much appreciated.