The Great Compromiser, Henry Clay, was the author of a major compromise between the free states and the slave states in the 31st Congress. Clay proposed a bill on 1/29/1850 which would accomplish several goals of each side, none of which could pass independently. The provisions were:
1) California would be admitted to the Union as a free state. This would upset the equilibrium between the free and slave states in the Senate.
2) New Mexico and Utah would be organized as territories, without reference to slavery. The free states generally hoped to keep slavery out of the territories, but the slave states recognized the need for extension of slavery into potential new states. This provision was consistent with Clay's earlier Missouri Compromise of 1820.
3) The boundary of Texas would be altered. The state would be reduced in size, and in return the USA would assume the former Lone Star State's debt.
4) The slave trade was banned in the District of Columbia, but slavery there would not be banned. This bill soothed northern congressmen who were appalled by slave auctions in DC.
5) A new Fugitive Slave Act was passed. This act greatly strengthened the old law through the appointment of federal marshals to streamline the process of returning captured slaves.
After weeks of debate, the omnibus bill was divided into smaller bills and passed separately between 7/31/1850 (when the Senate passed the New Mexico and Utah Territory bill) and 9/17/1850 (when the House passed the DC Slave Trade bill). Of all the smaller bills, the closest vote came on the Texas bill; it passed 30-20 in the Senate and 108-97 in the House.
President Fillmore signed the NM/UT bill into law on 9/9/1850 as the first of the smaller bills and completed the Compromise on 9/20/1850 when he signed the DC slave trade bill into law.