Final answer:
The people of Santa Fe, NM rejected Texas' claim of the border at Rio Grande because Mexico did not agree with Texas' claim and insisted the border lay at the Nueces River.
Step-by-step explanation:
The people of Santa Fe, NM rejected Texas' claim of the border at Rio Grande because Mexico, which formerly ruled over New Mexico, did not agree with Texas' claim. Mexico insisted that the border lay farther north at the Nueces River. From Mexico's perspective, allowing the United States to control land beyond the Rio Grande would mean an invasion of their sovereign territory.