Any help that Republicans get from the response by the Catholic leadership (and a lot of their followers) to attacks by the Obama regime, is purely incidental and not at all the objective in this death-match. They simply cannot absorb the frontal assault without striking back, much as the Catholic Church has never tolerated kings and despots in the past that have tried to dismantle the teachings of the Pope and Holy See.
The Catholic Church, and their separated brethren, the other Christian professions of faith, have successfully thrown out excessively restrictive regimes, be they kings, or dictators, or just fanatical warlords on a rampage. It is no anomaly that so many Christian hymns have a martial air, that the strong right arm of God calls forth so many human beings in righteous and thunderous wrath to promote the rule of justice and peace.
That’s more or less how I see it too.