Final answer:
California became a state 62 years earlier than New Mexico primarily because of the Gold Rush, which led to sudden population growth and the need for an organized government. Political considerations surrounding the issue of slavery versus free states, and the Compromise of 1850, also played a critical role in California's accelerated path to statehood.
Step-by-step explanation:
The discrepancy between when California and New Mexico became states is largely due to the Gold Rush that occurred in California. After the Treaty of Guadalupe Hidalgo in 1848, and the subsequent sudden discovery of gold, California experienced a massive influx of people, which accelerated its path to statehood. The rapid population growth led military authorities to push for an organized territorial government, and before Congress could act, California already had enough people to consider applying for statehood.
Meanwhile, political considerations also influenced the process. Matters of whether new states would be free or slave states were of pivotal concern, and California's entrance as a free state, following the gold rush, significantly upset the balance of power in Congress. The Compromise of 1850 was proposed by Senator Henry Clay to address these sectional tensions and allowed California's statehood as a free state. This compromise, while it resolved the immediate issue, did not settle the ongoing conflict over slavery, which continued to ferment sectional discord.
In contrast to California, New Mexico lacked the same economic stimuli and did not become a state until 62 years later. It faced its own unique set of political challenges and economic development pace that differed vastly from California.