What was Millard Fillmore's major challenge?

Answer 1

Dealing with the disputes over slavery - whether to allow slavery in the new states and what to do about returning fugitive slaves. He pushed forward the Compromise of 1850 which was not successful and satisfied nobody.

Answer 2

The biggest problem that Fillmore faced was slavery-- especially what to do about slavery in the new territories and what to do about escaped slaves and the people who helped them.