Could the atkins fitness program harm the heart?

Yep: Atkins' diet (not fitness plan) is essentially a caloric restriction based on eating only fats. The idea is that you'll feel full and/or sick before you get more calories than you need for the day. As atkins himself found out, it leads to premature heart disease and heart attacks. Meats are often cured with large amounts of salt too, so there's a decent chance of accelerated hypertension as well.