What was the popular support for US military efforts like throughout it's history?

I'll direct my answer at the Civil War. One could argue that American civilians were the most supportive, knowledgeable, and involved citizenry during the Civil War than during any other war in our nation's history. Regardless of which side they were on, American civilians were deeply connected to their soldiers for four reasons: (1) Units were raised, equipped, and deployed by locale. (2) Volunteerism was high during the initial stages of the war and was usually tied to honor, masculinity, and duty to their unit and home. (3) Civil War soldiers were arguably the most literate soldiers in the history of American warfare, writing and reading tens of thousands of correspondence from home, keeping them intimately connected to their loved ones and the home front. (4). American civilians, whether organized in either benevolent societies or as individual families, contributed more to the war effort than at any other time in our nation's history, with the possible exception of the Second World War.

First, historians like Peter J. Parish have argued that the Civil War (I'm paraphrasing here) was a war of small communities rather than one of organized nation-states. Civil War soldiers were initially raised and equipped by their towns and cities. As a soldier in 1861, you would probably volunteer and be integrated into a unit with your brother, father, family doctor, local representatives, and a few of the town's less reputable men, with your army services being provided by the town preacher, who could accompany you to the front. As the units were organized, families, groups of families, local politicians/bankers/merchants would buy the clothing and arms necessary to equip these units, before they would transfer to a state meeting point where they would join other units from their state. So already, we see armies organized by local communities that are then presented for state service, rather than like today where the federal government sends you to boot camp for training, equipment, etc. Though there was some variation to the way these things occurred, North and South, the armies of 1861 and 1862 were the largest locally organized forces in the history of America.

Second, many soldiers volunteered due to antebellum ideas of honor, masculinity, and duty to one's home and family. To not participate and contribute was viewed very negatively by both soldiers and civilians. Typically, a volunteers were viewed more positively than drafted men after 1862 in the South and 1863 in the North. Though, even drafted soldiers were largely supported by the homefront as well. In addition, since civilians had similar ideas of honor and duty (and also femininity), daughters, mothers, and younger sons wanted to contribute as well. Since they could not directly serve, they had to contribute in other ways. This will come up later in my fourth point.

Third, Civil War armies were probably the most literate armies in the world at the time, as seen by the tens of thousands of correspondence between them and the home front. This amount of correspondence shows a deep emotionally commitment from both soldier and civilian to each other. Soldiers would write home about the dullness of camp life, their health, the harshness of the march, the terror of combat, and etc. Civilians would write their soldiers about how they missed them, how they were coping at home, their health, going-ons in the town, gossip, news from the papers, and etc. This high exchange of information maintained an intimate connection between soldiers and their homes, that sustained both soldier and civilian during the trying times of war.

Fourth, civilians--either organized or independently directed--contributed more to the war effort than at any other time, with the possible exception of WWII. Northern benevolent societies ran and organized by both men and women, contributed to great increases in camp health that lowered death rates associated with disease and poor conditions. Southern nurses ran private hospitals out of their own homes, to care for wounded soldiers and the infirm. Both North and South, families sent care packages to the front, with clothing, weapons, food, and other necessities to improve their loved-ones morale and prospects.

One additional point to make, this description I have given, while accurate, was not universal and was also subject to change based on historical events. We have ample proof of the resistance to the war from Northern Democrats and Southern Unionists. In addition, triumphs of disasters on the battlefield, as well as political proclamations, could drastically alter the a person's position on the war. War weariness or a hatred for black emancipation could lead to a drop in support. While crushing victories could see a swell of support. It was all fluid and ever changing, much like today.

So, to sum up, because of the way units were raised and equipped, the role of ideas about honor and duty for both soldier and civilian, the high correspondence between the battlefield and the home front, and depth of contributions from families and benevolent societies; the Civil War represents a period of intense citizen support for the war and the soldiers who took part. However, this support was not always universal and was also contingent on historical events.

(Sources: Gallman, J. Matthew. The North Fights the Civil War: The Home Front. Chicago: Ivan Dee, 1994; Gallman, J. Matthew. Northerners at War: Reflections on the Civil War Home Front. Kent, OH: Kent State University Press, 2010; Parish, Peter J. The North and the Nation in the Era of the Civil War. New York: Fordham University Press, 2003; Parish, Peter J. “Conflict and Consent” in Peter J. Parish, The North and the Nation in the Era of the Civil War (New York: Fordham University Press, 2003): 149-170; Gallagher, Gary W. The Confederate War. Harvard University Press, 1999; McPherson, James M. For cause and comrades: Why men fought in the Civil War. Oxford University Press, 1997.)