The answer is "Yes. They did."
There is no rule in America that all citizens must support a common goal. There is instead a treasured freedom to speak your mind, however vacuous, insipid, or ill-informed. It is not the power of law that is called to reject such bleatings, but the power of common sense, the personal values of the listener who passes by the shameful, embarrassing soapbox.
As Vietnam showed and the current actions of [the left in America] regarding Iraq continue to demonstrate, it is extremely difficult to fight a 'long war' when you have an active 5th column in the media, academy and business and political elites that is stabbing the country in the back. If you think it's necessary to fight such a war, this column must be crushed: those actively engaged in treason (Code Pink, the Evergreen nutroots, etc.) need to be arrested and charged; those engaged in unseemly defeatism and anti-American protest in the street or in the acdemy need to be confronted using the bully pulpit, legislative hearings, etc., and shamed into shutting up or be booted out of their positions for turning the media and the academy into mindless left-wing propaganda organs.
We won the cold war through an accident of character: if Jimmy Carter had been a little better domestically, the Soviet Union would have established complete hegemony and would probably still exist.
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So, no, they didn't fight to allow traitors to go unpunished and the contemptible to be praised.