In a large pot, combine 1-½ cans of the broth, tomato sauce, chili powders, cumin, and 1 teaspoon salt. Bring to a boil, then reduce the heat to a simmer.
Meanwhile, in a large skillet, heat 1 teaspoon of the oil and saute the onion and garlic over low heat until tender. Add to the sauce. In the same skillet, adding oil as needed, saute the meat, one-third at a time, until no longer pink. Add to the sauce. Bring to a boil, reduce the heat, and simmer for 2-½ hours, adding more chicken broth as needed. Thirty minutes before serving, add the Tabasco and salt to taste.