Cook the sausage in a skillet over medium heat until fully browned. Drain off any excess grease.
Transfer the cooked sausage to a small slow cooker.
Add the undrained diced tomatoes and green chilies, the drained diced tomatoes and green chilies, the cubed processed cheese, and the cubed cream cheese to the slow cooker.
Stir the ingredients together gently.
Cook on low for 2 hours, stirring every 30 minutes until the cheese is completely melted and the dip is smooth.
If the dip is too thick, stir in milk, one tablespoon at a time, until you reach your desired consistency.
Serve warm directly from the slow cooker.
Notes
For a real cheese version, substitute the processed cheese with 1 pound of shredded sharp cheddar cheese and 4 ounces of Monterey Jack cheese. You may need to add a little extra milk for smoothness.
You can prepare this dip ahead of time by assembling all ingredients in the slow cooker the night before, keeping it refrigerated, and starting it on low 3 hours before serving.
Serve with tortilla chips, sturdy crackers, or vegetable sticks for dipping.