So, for the sake of this discussion, let's divide the North up a little into different units. The first unit will be the soldiers in the Union Army themselves (with the exception of officers). The soldiers of either side of almost any war are often convinced before the fighting ever even starts that their side will be victorious.

The officers (unit 2) though, were a little more uncertain. General McClellan, for example, was kind of notorious for sitting on his hands and waiting. To the extent that Lincoln himself had to sometimes prod him along and force him to make a move. I forget the quote exactly but it was something like "if McClellan had a million men, he would convince himself that the the other side had two million and wouldn't move until he had three million, but he would then convince himself the other side had four." Anyway, it is a small example but it conveys that the officers themselves were unsure.

Lincoln and other politicians (unit 3), likewise, were unsure. They often spoke with a sort of pressing urgency as to the necessity of making sure the Union stays intact, but they had no illusions that their victory was cemented.

Women in the North (Unit 4) were also diverse in terms of outlook on victory. Many had faith that their husbands, fathers, and brothers would come home victorious. Other women had a more morose perspective.

To make this a more nuanced answer, also consider what it took to be victorious. Officers in the North recognized pretty early on that to defeat the South required the defeat of an entire ideology: a true conquest really. It wouldn't really be enough to just cut off supplies or kill a bunch of people, they had to destroy the ideologies that drove them. Slavery, for example, was more than economic--it was the social glue of the South. Anti-big government, likewise, was part of the South's social and cultural structure. Anyway, add all of this up (and more) and victory becomes a hugely difficult thing for the North to acquire.

Furthermore, look at the war itself. The first couple of years saw some major Confederate victories. Enough that Union victory was by no means taken for granted. It wasn't until 1863/1864 that the tables turned enough that the North perceived themselves as putting the South up against the ropes.

Anyway, this was a really short answer but hopefully provided some new perspective concerning your question. Much of the information above was drawn from the following sources:

-"The Union War" by Gary W. Gallagher -"What this Cruel War was Over" by Chandra Manning -"The Fiery Trial: Abraham Lincoln and American Slavery" by Eric Foner