Broil the poblanos on a foil-lined pan, turning, until blackened all over, 8 to 10 minutes; cover them for 5 minutes, then peel, seed and dice them.
Season the chicken with 1 tsp salt and place it in a 6-quart slow cooker with the poblanos, onion and garlic.
Mash one can of beans with 1/2 cup broth and add it to the cooker with the whole beans, remaining broth, green chiles, cumin, oregano and remaining salt.
Cover and cook on low until the chicken reaches 175°F and shreds easily, 5 1/2 to 6 hours.
Remove and shred the chicken, then return it to the cooker with the corn and cream cheese.
Cover and cook on high for 20 to 30 minutes, stirring twice, until the cheese melts smoothly and the corn is hot.
Stir in the lime juice and check the salt before serving.