In this question, we do not know what the sentences in bold are. However, this is not necessary in order to understand the meaning of the passage.
In this passage, Abraham Lincoln describes his thought process when it came to dealing with the issues of the Civil War. He tells us that he was faced with a difficult decision, as he needed to decide whether to admit that the Union was lost and that the Confederacy should leave, or to focus his efforts on the "colored element." This refers to slaves. He argues that he chose the latter.
This indicates that President Lincoln did not want the Union to split up. The Confederacy had left the Union because of several disagreements, mainly the issue of slavery. However, Lincoln was unwilling to accept that the Union could be disintegrated and that the South could chose to not follow the Constitution. He acted in accordance with these goals.