Stir together cheese and 3 cups of water in a double boiler over gently simmering water; stir occasionally until the cheese has melted and the mixture is smooth.
Meanwhile, combine the 1/4 cup of water, onion, celery, green pepper, and jalapeno in a medium saucepan; bring to a simmer over medium heat. Whisk the vegetables into the cheese, then pour the mixture into a large pot; place over medium heat and simmer for 5 minutes.