I believe it was just the Army, not the whole military. And “Following a discussion between Archbishop Broglio and the Secretary of the Army, The Honorable John McHugh, it was agreed that it was a mistake to stop the reading of the Archbishops letter.”
“There SHOULD be civil disobedience - MASSIVE civil disobedience - before it is too late!”
That's fine, but if you're an officer in the military, the last I heard, you protest by resigning your commission. And if you engage in civil disobedience, you should expect resistance whether you succeed or not. (Well, maybe not if you're an OWS type or something similar.)
By the way, just so we'd know what we are discussing, do you have a link to a copy of the actual letter in question?
http://www.diocesephoenix.org/uploads/docs/RELIGOUS-LIBERTY-INSURANCE-LETTER-013012.pdf
http://www.milarch.org/site/apps/nlnet/content2.aspx?c=dwJXKgOUJiIaG&b=7656203&ct=11609821