The peace democrats were a much bigger political problem in 1863 and 1864 -- up until "little Napoleon" was beaten by absentee balloting....passed by Congress without demur. There were Democrats on the roster in 1861 but they were not a real factor. Certainly there wasn't enough of an active effort by them to derail anything else Lincoln was doing for the war effort. I simply do not see why it took them (and it should have been them not Abe) to issue the suspension resolution.
You are absolutely correct that a lot of things get tossed on their ear in a civil war.
Bookmarks