You are mischaracterizing things. Sure, Lincoln disagreed, but most of the people in the remaining Union were okay with it until the Attack on Ft. Sumter. Northern newspapers of the time were publishing editorials that said stuff like "Go in Peace our Bretheren" and such.
The Union WAS NOT opposed to Southern Secession until Lincoln stirred them up to oppose it.
I don’t think it is at all accurate to say that “most of the people in the remaining Union were okay with it.’
Most people in the Union were opposed to secession, but were very divided about how to respond. Almost nobody wanted war, but the question of exactly what should be done was hotly debated.
For obvious reasons, Democratic party newspapers and such were the most likely to oppose “coercion” as a forceful response was called.
Meanwhile, Davis and the CSA was faced with the possibility that seceded states might begin to drift back towards unionism.
However, the major issue dominating the scene between the founding the CSA and Sumter was the unseceded slave states. Everything Lincoln and Davis did was essentially a giant-stakes poker game to see who would win those states.
In the event, they wound up splitting the pot. Which meant that we’d have a long, bloody war rather than a short one.