Place the chopped vegetables, beans, green chiles, and chicken in the crock pot.
Sprinkle the salt, chili powder, paprika, garlic powder, cumin, black pepper, and cayenne pepper over the chicken and veggies, then pour the chicken broth over all. Cover and cook on low for 8 hours or on high for 4 hours.
When there are 30 minutes left on the cooking time, add the cubed cream cheese, re-cover, and continue to cook. Stir in the melted cream cheese until no lumps remain.
Remove the chicken to a cutting board and shred with a fork. Return the shredded chicken to the slow cooker, and add the lime juice. Stir well and serve immediately with sour cream, cheese, and the other toppings of your choice.