Final answer:
The statement is true. Various incentives including the pursuit of precious metals and generous land grants led to the establishment of Spanish settlements in New Mexico, notably Santa Fe in 1610, with continued attraction for settlers in later periods under Mexican governance.
Step-by-step explanation:
The statement that thousands of Spanish settlers were attracted to New Mexico is true. In the context of New Spain, which included territories such as New Mexico, there was a concerted effort by the Spanish crown to encourage settlement. Initially, the search for precious metals was a significant lure for settlers, but even after it became clear that the territories did not contain abundant gold and silver, land grants and the prospect of wealth through landownership and agriculture continued to attract Spanish settlers.
Santa Fe was established in 1610, reaffirming the Spanish presence in the area. Over time, not only Spaniards but also other Europeans and Americans were drawn to the region, attracted by the generous terms for land acquisition offered by subsequent Mexican authorities after Mexico gained independence from Spain. This influx was heightened by the belief in the United States in the concept of 'Manifest Destiny', which held that American settlers had a divine right and national purpose to expand their territory across the continent.