Joe comparing Mrs. Joe not wanting him to be educated to the government implies the government’s denial of education to the poor.

There are many elements of satire in the book.  Satire is when the author makes a joke with a purpose.  In this case, social and political satire is employed.  When Joe says that Mrs. Joe is given to government and does not want him to be able to read and write, it implies that the Victorian government tried to keep poor people down by denying them education.

“And she ain't over partial to having scholars on the premises,” Joe continued, “and in partickler would not be over partial to my being a scholar, for fear as I might rise. Like a sort of rebel, don't you see?” (Ch. 8)

Education of the poor was one of Dickens’s pet peeves, addressed in many of his books.  In Oliver Twist and A Christmas Carol specifically, he highlighted the effects on society of not educating the poor.  When Joe makes this comment, it is a joke.  Yet it was a real issue to Dickens, and education was important to him.  He believed that the poor had a chance to be happy and comfortable, just like everyone else.  The treatment of them by the British government, specifically the Poor Law, infuriated him.