Based on the historical context, the United States wants the southern Texas border to extend to the Rio Grande.
Following the independence of Texas from Mexico, there were disputes between the southern border of Texas, between Mexico and Texas.
Mexico claimed the border stopped at Nueces River, while Texas, supported by the US government, declared it stopped at the Rio Grande.
This led to Mexico-American War in 1846, in which, at the time, Texas had been annexed as a state in the United States.
Hence, in this case, it is concluded that the correct answer is "Rio Grande."
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