What I'm guessing is going on (but can't know without seeing the data) is that your explanatory variables are highly correlated with each other. The significance of each variable is calculated based on how much additional variance is explained when you add that variable to a reduced model with all the variables except that one. So if your explanatory variables are collinear, adding another one isn't going to explain much variance that the others haven't.

Also, definitely too many predictors for the data you have. That could, quite possibly, be the sole reason your explained deviance is so high. For only 12 data, you probably don't want more than one or two predictors (though read elsewhere for other opinions).

One possible way forward would be to do a principal component analysis of your explanatory variables, or of a subset of your explanatory variables that would naturally group together. If one or two principal components explain a large proportion of the variance in your explanatory variables, then use those principal components as your predictors instead.

Another possibility would be to jettison any predictors that seem less important a priori (emphasis on the a priori part).

Also, you will probably get better answers than this on Stats.SE.