Common Sense was the official publication of the Independence Party, which in turn was suspected to be the public face of the Sons of Liberty paramilitary group. Its publisher was John F. Kennedy of Boston, Massachusetts.
The authorities of the North American Union regarded subscribers of Common Sense with suspicion. Kathleen Flannery was listed as a subscriber, but it was her father Aloysius Flannery who insisted on buying the subscription for her. When Thomas Bushell questioned her on it, she claimed it reflected her father's politics, not hers, and that she would only occasionally glance through an issue.
In OTL, Common Sense was a pamphlet written by Thomas Paine and published anonymously on 10 January 1776, during the American Revolution. It encouraged a complete break from Britain at a time when the question of independence was still undecided.
In The Two Georges, colonial grievances with Britain were resolved sometime before 1770, averting any reason for Paine to write this pamphlet. As Paine is mentioned nowhere in the novel, there is no reason to presuppose that the phrase "common sense" has any connection to Paine within the Georges' universe.