I have taken cheese into the US many times; from ARG,Chile, Italia, etc... The issue is hard vs soft cheese, and also if soft, then is it pastuerized? unpastuerized soft cheese is NOT allowed. If it is soft cheese, then it must have a label that states it has been pasteurized on it. Soft pasteurized cheese is allowed. All hard cheeses are allowed.
I always declare the cheese on my customs form. I usually take in 1/2 round or a full round of cheese. The only place i have been stopped was entry into Chile from ARG with cheese. They have dogs that check the luggage, so the officials opened my bags. Everything was fine as the soft cheese was pasteurized.