There's some good news for cougars, especially compared to other wild felines, which have far more trouble dealing with habitat loss and other factors which threaten populations.
Cougars are rated "least concern," which means they don't face immediate threat of extinction. Although exact numbers are always difficult, scientists estimate that about 50,000 cougars live in the wild, and this relatively large population, as well as their wide range and adaptability to a variety of habitats, is part of what gives the mountain lion a good chance at surviving for a long time.
However, that doesn't mean it's time to stop worrying. Cougars face a serious threat from hunters, especially in the United States, where some states don't even have laws against hunting them. Farmers sometimes consider them a threat to their animals, and will hunt and kill them to protect their farms.
Over in Florida, cougars are critically endangered. This population, called the Florida panther, is the only known surviving population of cougars in the eastern United States, and survival is very challenging when cut off from other breeding populations.
If the cougar is going to survive in North America, serious conservation efforts need to be improved, especially in areas like Florida, with such a low population, and Texas, which seems to have no laws regulating cougar hunting at all.