The argument is that once a part of the Federal system, Congress reserves the right to guarantee that the States are run by a Republican form of government. If the States withdraw from Congress, and their legislatures along with their militia lay siege to facilities previously placed under Federal jurisdiction - that is an instance where Congress and the Executive are bound by the constitution to step in - using the Militia laws of 1795 and 1807 to enforce Federal Law using levies drawn from the other states.

The enthusiasm to abolish slavery doesn't seem to have been universal. I recall reading somewhere (maybe the Heintzelman diaries) about a Federal unit out west that refused to serve after the Emancipation Proclamation was announced. Most people in the North were probably just insulted that the South didn't follow the law after they had largely outweighed the North during the drafting process. When the North finally won the executive branch, the South preemptively seceded and fired on their northern neighbors who refused to abandon their posts. That's just not civil.