A reconstruction of what a modern, featherless descendant of a Troodon might look like.
After thinking some more about the topic, I have come up with a new hypothesis about sightings of bipedal dinosaur-like creatures in the United States. I now think it's possible that they might actually be surviving descendants of troodontid or dromaeosaurid-like dinosaurs. I will now explain what led me to this conclusion.
First of all, after reading this fantastic article by Scott Mardis, I have become much more open-minded about the Prehistoric Survivor Paradigm (PSP).
As Scott pointed out in his excellent article, there are many examples of Lazarus taxa (creatures which disappear in the fossil record, only to appear again much later) and ghost lineages (the missing fossils that are in between the Lazarus taxa). A good example from Scott's article was the megachasmids (a group of sharks which includes the modern Megamouth Shark). Fossils of megachasmids are found in the mid-Cretaceous, but then they disappear. They do not appear again until the Miocene, 70 million years later. So there's no reason why dromaeosaurids or troodontids also could not have left a 66-million-year ghost lineage from the end of the Cretaceous until now.
And actually, according to this article, a fossil tooth of a Velociraptor-like dinosaur was, indeed, discovered in Miocene deposits in Louisiana. It is possible that it was just reworked from older sediments; however, there still remains a distinct possibility that it actually was native to the Miocene, and that it is evidence of the survival of small theropod dinosaurs beyond the end of the Cretaceous.
(By the way, it is worth noting that there are actually a lot of plesiosaur remains from the Cenozoic that are supposedly "reworked". These remains range from the Paleocene to the Pleistocene, and according to some researchers, such as Scott Mardis and Dale Drinnon, there is sufficient evidence to suggest that they are not really reworked, and that they are actually native to the Cenozoic.)
For the most part, the creatures described in the sightings very much resemble a Troodon-like dinosaur, except for one major difference: they lack feathers. It is now believed that troodontids, dromaeosaurids, and their relatives had feathers, like modern birds. And almost all sightings of these bipedal dinosaur-like animals describe them as having scaly, featherless skin.
However, I have found that even this difference is still reconcilable with a troodontid identity. Many birds alive today have lost their feathers and replaced them with scales, so there is no reason why troodontids also couldn't have done the same. There could be many possible reasons for the loss of feathers.
One hypothesis, which I think is the most likely, is that they lost their feathers due to adaptations to a semi-aquatic lifestyle. These creatures are said to live around bodies of water, and are said to be somewhat semi-aquatic. This is why they are often referred to as "River Dino" and such.
When animals start to live in the water more, they often lose their fur or feathers. For example, whales are descended from furry ancestors, but they have now lost almost all of their fur. Penguins are an example of modern birds which are semi-aquatic, and they already have shorter feathers than other birds.
And it's possible that not all of the feathers have been lost, and some of them still remain.
Perhaps they still have some feathers left on their backs, for example. This could explain why so many witnesses claim that they have spine-like structures on their backs.
So this is my hypothesis. I would very much appreciate any constructive critiques or suggestions.
P.S.: I am not completely in support of this hypothesis. It's just a possibility that I'm throwing out there.