The will to fight may have been there but no war works unless you have the logistics to fight it, whether a guerilla war or not, and when the enemy occupies your homeland and whatever means of production you may have had those logistics have to come from somewhere else. The Northern blockade of the South was very effective and after a general surrender by the officially recognized Confederate government* no European country was going to support a hopeless force. Supplies could have come through Mexico by some foreign power interested in annoying the USA but with the limited mobility of the time operations could only extend a relatively short distance from the Mexican border.
It's possible that an organized albeit limited guerilla force could have been sustained but to what end? Who would they kill except for hit and run raids against the occupying forces who were already becoming used to dealing with Comanches, Sioux and other extremely talented light cavalry forces? That, plus invariably the "if you ain't 100% with me you're 100% agin' me" attitude would have prevailed among the guerillas and their tactics would have devolved into terror attacks against the local populace, ala the Viet Cong's and the Khmer Rouge's atrocities against the native populace.
After Lincoln's death the overwhelming mood of the North was to punish the South in every way possible. They weren't about to quit and go home because some border outposts were sporadically raided, instead they would have stomped their boot on the South in an even harsher manner. So now you have a small group of people continuing a war folks were sick of, that causes the Yankee invader to enact harsher and harsher reprisals, plus the guerillas are killing your friends and neighbors.
Guerilla wars work as a nucleus or spark of a general revolution, they can be carried on indefinitely when they have a reliable source of weapons and supplies and most of the country supports them or at least doesn't act against them, but they only prevail when the people of the foreign power get sick of the war and eventually decide to go home. Though the South viewed the North as a foreign power the North considered the South as part of one country, there was no foreign home to go home to, they were just reintegrating a part of their previously unified country. In 1865 conditions just weren't there to support that type of warfare.
* my memory is sketchy here, but I don't believe any foreign power ever officially recognized the Confederate States as a legitimate government. England was thinking about it but that whole slavery thing kind of made them shy away.
