Longer Civil War -- Tip a couple states or European Involvement
Two possibilities:
1) One or two states that remained union decided to go (or were allowed to go) Confederate. Best candidates would be Kentucky or Maryland. As noted, Kentucky would have improved the Confederate position substantially. Maryland was, in part, prevented from going confederate because it would have made DC untenable, but it's possible that heavier Union losses early on could have provided a path for some/all of Maryland to join the Confederacy. That would have greatly weakened the union, but might have actually ended the war early becuase the Union might have been more or less forced to come to terms.
2) European involvment. If France and/or Britian had supported the Confederacy in 1862 or so it could have extended the war by limiting Union capability to blockade the South or conduct some of their pennisular movements (perhaps trapping a Union army there). A supply of French/British weapons, gunpowder, and money would have strengthened them considerably and, perhaps, have prevented the victory Lincoln needed to issue the Emancipation Proclamation. Then, the war might either have dragged on or ended earlier (with the Union coming to terms).