Put the months in quotes, they are strings, furthermore the auxiliary variable a is not needed:
color[monthSwitch_] :=
Switch[monthSwitch, "January", "01", "February", "02", "March", "03",
"April", "04", "May", "05", "June", "06", "July", "07", "August",
"08", "September", "09", "October", "10", "November", "11",
"December", "12", _, monthSwitch]