If you are reasonably assured that you won't take a shot beyond, say, 300 yards, the .30-'06 is most definitely "enough gun" for legal hunting in the lower 48. So are many other cartridges, including the .308.
(There are the exceptions of the feral cattle in the canebrakes of the lower Rio Grande, and the Nilghai of the King Ranch, in Texas. There, such as the .338 and African cartridges become highly desirable.)
If you drop back to, say, 200 yards, you get into .243 and .30-30 country.
Again, here, I'm talking about the average hunter/shooter. There are always some who are well above average; there are some who couldn't hit a bull in the butt with a bass fiddle if they were locked in a closet.
You're from BATFE? Come right in! I use all your fine products!