Final answer:
The failed attempt by Congress to settle the slavery issue during secession was the Crittenden Compromise.
Step-by-step explanation:
The failed attempt by Congress to settle the slavery issue as southern states started seceding from the Union was the Crittenden Compromise.
Proposed by John J. Crittenden of Kentucky, the compromise included renewing the enforcement of the Fugitive Slave Law and allowing slavery to continue in the nation's capital.
However, the Republican Party, which had just gained power, did not accept these terms, and southern states proceeded with their plans to secede from the Union.