Although it would certainly help if the Members of Congress did have a conscience and did take seriously the sacredness of their oath, that's in no way necessary for the success of the "You Swore on the Bible" strategy.
The strategy of "You Swore on the Bible" is not one of a private communication, in which an appeal to conscience is made. It is an entirely public statement, intended to apply pressure on the Members of Congress by affecting how they are perceived --and thus also how they are regarded-- by their constituents.
These people get elected to Congress by persuading the public that they are upright, patriotic, God-fearing people. How can you be God-fearing if you break a promise made before God --if you can commit "a crime against God"-- and think nothing of it? How can you be a patriot if --by violating your oath of office-- you indifferently commit a treasonous act? How can you be upright if your promises mean nothing?
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