What strategy did the north have after they got defeated by the south?

The South's strategies after Antietam were centered around delaying the Union as much as possible while persuading England, France, and Netherlands to recognize them as a nation. The South also wanted to hold out two more years until the 1864 elections, when they were sure that Lincoln could be ousted and the war ended. Militarily, they planned at least one more attempt at invading the north in an effort to topple Lincoln militarily.

The success of any of these three strategies would have likely resulted in an independent Confederacy and continuation of slavery for at least another generation.