Texas mostly occupied land east of what is now I-35 and north of the Nueces River. Mexico claimed the Nueces River as the boundary between Texas and Mexico. Texas claimed the Rio Grande as the border. When the US annexed Texas at the end of 1845, the Polk administration adopted Texas' claim. Nueces County, which is located south of north bank of the Nueces River, was organized by the State of Texas in 1846 to advance the Texas claim to the land located between the Nueces and Rio Grande Rivers.
The fence is mostly going to be in New Mexico, Arizona, and California which were not part of the US till after the Treaty of Guadalupe Hidalgo but had been occupied by US military forces since 1846. It wasn't Texans primarily who took that territory from Mexico.
Watching the History Channel documentary about the Mexican-American war I see :)
I know all of that-I may not have made it plain in my post because I am tired- long day and it is getting past my bedtime.
I was speaking in general terms. Many people don't realize Texas was a seperate country for a while; and not acquired the same time as the land the US bought in the Hidalgo Treaty and the later Gadsden Purchase. You of course are right that most of the issues of the border boundary were settled with the Treaty de Hidalgo- but not all of course which is why the Gadsden purchase was needed. We almost went back to war w/Mexico then too.
The actual boundary of what exactly was the Republic of Texas differed at the time, the arguement over that and a few other things is why the Mexican War was fought.
The proposal for this 700 miles of fence that I saw does include part of the Texas border- I didn't really pay attention to what part(s) I was mostly concerned with my area when I read it and we are going to be in a gap between two long stretches if they passed what I read.