A k-total-coloring of G is an assignment of k colors to the edges and vertices of G, so that adjacent or incident elements have different colors. The total chromatic number of G, denoted by χ (G), is the least k for which G has a k-total-coloring. It was proved by Rosenfeld and Vijayaditya that the total chromatic number of a cubic graph is either 4 or 5. Cubic graphs with χ= 4 are said to be Type 1, and cubic graphs with χ= 5 are said to be Type 2. A k-total-coloring is equitable if the cardinalities of any two color classes differ by at most one. Similarly, the least k for which G has an equitable k-total-coloring is the equitable total chromatic number of G, denoted by χe (G). It was proved by Wang that the equitable total chromatic number of a cubic graph is either 4 or 5. We investigate two questions about total colorings of large girth cubic graphs. 1. Does there exist a Type 2 cubic graph of girth greater than 4? 2. Does there exist a Type 1 cubic graph of girth greater than 4 with χe= 5? We contribute to both questions by exhibiting infinite families of cubic graphs that indicate that possibly both questions would have a negative answer. In par-