Cougars seem to be doing well, and are (slowly) expanding their range eastward...a few males have wandered as far as Illinois. Been an increase in sightings in Wisconsin. No breeding population but they are definitely present in the state. There have been increases in human-cougar conflicts in increasingly urban areas such as southern California and Colorado, but the fact they can persist at all in those areas is a testament to their hardiness.
I haven't heard any suggestion that cougars and wolves compete. Both species almost completely overlap in range and are very different in ecology. Certainly there is no shortage of prey in most areas.
If you want to worry about wild cats in the US, worry about the Ocelot: the proposed border wall has a good chance of eradicating the final US populations via habitat destruction and preventing movement between populations.
World: 1195, ABA: 628
Last Lifer: Connecticut Warbler
Last ABA: Connecticut Warbler
Mammal: 233 Herp: 174