Well, this is one time when I believe in substituting something in a recipe without a second thought - real cheese for the processed cheese.
Here is GB's recipe for Queso Blanco
If you look at the recipes from the link I gave you and compare them - they are similar.
I don't think I've ever gone by a recipe - but, it goes something like this:
2 Cups cheddar - grated fine
1 can RO*TEL Tomatoes and Green Chilies or your favorite bottled Pecante Sauce
1-2 tablespoons butter
about 1/2-1 cup cream, or milk
Put the butter, Ro*Tel tomatoes and grated cheese in a double boiler and heat until the cheese is melted - stir frequently with a wire whisk. If it is too thick - thin with some cream or milk.
If you don't have Ro*Tel tomatoes and chilies - use your favorite pecante sauce. Or, you can even use your favorite homemade salsa - although I don't like cilantro in my chili con queso.
You can even brown some crumbled hamburger meat with some diced onion, drain it, add some taco seasoning and add that - or use drained crumbled sausage.
Hey, it's just melted cheese, onions, tomatoes, chilies, and something to adjust the thickness (milk or cream) and added butter for a velvety richness. Adjust the ingredients to your liking - heck even add some garlic powder if you want, or some finely minced jalapeño peppers. Dad used to make it with a white cheddar-jalapeño cheese he brought back from Mexico when he was going down there a lot.