Don't Expect It to Last Much Longer Than Dec. 13th
From the beginning, Naughty Dog said that the start and end dates for the beta were subject to change. The start date has already changed and we could see the company extend the beta beyond December 13th. We've seen this happen with several betas including TreyArch's Black Ops 3 beta.
If this happens, we wouldn't expect it to last much longer than December 13th. If an extension happens, we'd expect it to be a day or two. We'd also expect the developer to confirm an extension late in the Uncharted 4 beta process.