At the time of Antietam, the Copperheads were at the height of their political strength, so I don’t see it as clear cut as you seem to, WA.
Ohio, Indiana, Wiscounsin, Michigan were all leaning to the copperhead viewpoint in large percentages at that time.
You are absolutely right - which is why President Lincoln issued the Emancipation Proclamation in Antietam's wake: to create an unbreakable hard core of war loyalists among abolitionists and strong federalists.
The 1862 House elections were weeks away and the President was concerned that the Copperhead/Peace Democrats might even win a majority in the Congress.
The Republican/Unionist alliance of course won - demonstrating that there was the political will to resist despite serious military setbacks.
Ohio, Indiana, Wiscounsin, Michigan were all leaning to the copperhead viewpoint in large percentages at that time.
Indeed they were.
But the 1862 elections showed that New England was rock solid for the Union and it would continue to ensure a pro-Union majority.