From independence (1836) through annexation by the United States (1845), Texas claimed the Rio Grande as its southern and western boundary. The Treaty of Guadalupe Hidalgo in 1848 confirmed the Rio Grande as the border between Mexico and the United States from the Gulf of Mexico to the 32nd parallel (just above El Paso). Texas insisted its boundary continued further along the river however, to its source in Colorado and from there north to the 42nd parallel. That is, Texas claimed 2/3rds of New Mexico including Santa Fe, much of southern and central Colorado, part of Wyoming, southwestern Kansas and the Oklahoma panhandle. See map.
As part of the Compromise of 1850 the boundaries of Texas were established as we know them (poor surveying and meandering rivers not withstanding), Texas received $10 million in compensation applied toward its debt (roughly $200 million today), and the Territories of New Mexico and Utah were established.