Why could southern politicians be considered over-optimistic in accepting this deal? what might they have been hoping for in the future if they supported the spread of slavery?

They ensured a huge free-state like California while giving the regions a chance to decide in favor of themselves.  

They trusted the regions would cast a ballot to permit subjugation.  

They trusted that if the regions cast a ballot to permit subjugation they would hold an enormous populace and various states the regions made up more land than California.

it is the code of hammurabi

roosevelt believed that in light of the country's recent military successes, it was unnecessary to use force to achieve foreign policy goals, so long as the military could threaten force. this belief, and his strategy of “speaking softly and carrying a big stick,” shaped much of roosevelt's foreign policy.