It is possible to have a final score of 6-1 in an NFL game. This is because the NFL allows six points to be scored in the form of a touchdown and one point to be scored in the form of an extra point or a two-point conversion. There are also other scoring opportunities such as field goals, safeties and a two-point safety which could also result in a 6-1 scoreline. Therefore, a 6-1 scoreline is indeed possible in an NFL game.