But empirical evidence does not need to be quantitative. There is plenty of evidence that the French lost Algeria when the French public lost faith in both Algerie Francaise and the French Army. There is also a lot of evidence that opposition to the Vietnam War aided the VC/NVA in their cause by influencing US policy and actual support to the RVN. The survey data do correlate with policy.

Finally, this issue is all part of the war for legitimacy which is fought in the country where the war takes place, the countries that support the "host government," and the "court of world opinion." (Sorry about the shorthand.)
To frame my question a bit differently, is opposition to a war necessarily bad? Furthermore, can opposition and dissent be in fact patriotic? There's a book out there about the liberal left reclaiming the patriotic high ground, and I believe that there are folks who have responsible and mature viewpoints about our global power and its repercussions.

And I do firmly believe that the road to war matters even more as we move along the timeline, because the venture of war will always take a toll in "precious treasure". We need to focus on moving to an endstate, for sure, but it doesn't mean we stop dissecting how we took that path in the first place.