Do the physicians "buy in" to case management? That's the first thing that needs to happen.
Instead of having the approach of having the patients "change their bad habits", take it one step at a time.
Start simple. For the heart failure patients, have them weigh themselves daily, and when their weight goes up quickly, ask the doctor for a bump up in their diuretic for a few days, and follow up closely. When the patient sees concrete results, they will begin to trust you. For the diabetics, have them check their blood sugars every morning, and then when they are doing that, have them check before breakfast and 2 hours after. Get their blood sugars under tight control, and when their HbgA1C is improved, show them the correlation to controlling blood sugar and the drop in HgbA1C.
When you introduce yourself, don't ask if they want a case manager. Instead, say I'm Joan Smith, the case manager in Dr. Jones' office, and I'm calling to see how you are doing". It's all about presentation.
As you gain their trust, you can increase your management, and you will find that more and more will be open to having you call.