He is referencing the issue of slavery and the threat of it being outlawed in the United States. This fear was very real for southerners after President Abraham Lincoln was elected president in the election of 1860. Southerners feared that he would outlaw slavery across the United States.
This issue greatly affected the southern states, causing several of them to secede (leave) the US in order to form their own country. This would be called the Confederate State of America and this faction helps spark the Civil War.
I would say conquistadors
Appointing a new justice to the supreme court.
Three-fifths
Here's the specific statement from within the Illinois Constitution (Article IV, Section 9): <em>The house to which a bill is returned shall</em><span><em> immediately enter the Governor's objections upon its journal.
If within 15 calendar days after such entry that house by a
record vote of three-fifths of the members elected passes the
bill, it shall be delivered immediately to the second house.
If within 15 calendar days after such delivery the second
house by a record vote of three-fifths of the members elected
passes the bill, it shall become law.</em></span>