The only part of the Compromise of 1850 that was strongly supported by the South was th newly implemented Fugitive Slave Law.
This Fugitive Slave Law made it so that any slaves who escaped to the North must be returned to their owners in the South. The goal of this law was to help limit the amount of slaves who escaped from the institution of slavery.
The other parts of the Compromise of 1850, including making California a free state and banning the selling of slaves in Washington DC, were not well liked by southerners.