In a medium bowl, mix the processed cheese, Cheddar, Monterey Jack and mozzarella. Set aside.
Heat the oil in a medium pot over medium heat. Add the sausage and cook, breaking into very small pieces with a wooden spoon, until browned and cooked through, about 5 minutes. Transfer the sausage using a slotted spoon to a plate. Leave the drippings behind in the pot. Add the jalapenos to the drippings and continue to cook, stirring, until the pepper has softened, about 2 minutes.
Sprinkle the flour into the pot and continue to cook until lightly toasted, 1 to 2 minutes. Add the chili powder and cumin and continue to cook until well incorporated to the flour mixture, 30 seconds longer. Slowly pour in the milk and cook, whisking occasionally, until smooth and slightly thickened, about 5 minutes. Add the cheese mix a handful at a time. Cook, whisking until smooth. You can add the next handful once the previous handful has melted about halfway.
Remove from the heat and stir in the browned sausage, 1/2 teaspoon salt and the pico de gallo. Taste and adjust the seasonings and heat with additional salt and hot sauce. Serve warm with chips for dipping and extra pico de gallo on the side.