New Mexico's challenges during their bid for statehood was mainly caused by Texas. Texas was getting annoyed by New Mexico for petitioning for statehood.
This is only one issue but I hope it was helpful.
partisan politics in both New Mexico and in Washington, D.C marked by distrust of New Mexico’s fundamentally foreign culture led to strong opposition that prevented the territory from joining. There was also reluctance among New Mexicans to take the leap towards statehood
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