Heat the vegetable oil in a large saucepan over medium-high heat. Add the onion and poblano and cook, stirring, until softened, 5 to 8 minutes. Add the tomatoes, garlic and cumin; season with salt and pepper. Cook until the liquid thickens, about 3 minutes. Add 5 cups water. Increase the heat to high and bring to a simmer, then reduce the heat to maintain a simmer and cook 10 minutes.
Meanwhile, combine the chorizo, crushed tortilla chips, cilantro and a pinch each of salt and pepper in a small bowl; mix with your hands until just combined. Form into 1-inch meatballs (about 20).
Add the meatballs to the soup and simmer until just cooked through, 5 to 8 minutes. Remove from the heat and season with salt and pepper. Ladle the soup into bowls; top with the cheese and cilantro. Serve with lime wedges and tortilla chips.