This is a bit of a grey area though. Mexico had quite a large border dispute with Texas (who was still not recognized by it). A succesful Mexico in the Mex-Am War should be able to keep some of this territory, the Nueces strip and the trans-Pecos region. So yes, the OP isn't wrong on its post the US is getting a smaller Texas from Mexico; by itself Texas could only give it the "core" territory.
It depends how little, or how the war ended. The primary goal of the US was getting Texas and the "useful" part of California, which gives them access to San Francisco and Monterrey Bay (they got more than that in OTL).
If the US gets a border where they keep most of Texas and then a straight line border from the Pecos river to the Pacific at the 37th parallel (this border was proposed by Jose Joaquin Herrera to avoid the war, but he was deposed at the start of the war). Another, option is the 35th parallel so the US gets northern Arizona/New Mexico, and the San Joaquin valley in Califonria, including Monterrey Bay; Mexico only keeps the southern "cow counties". Depending on how the war ended, the US should be satisfied in both cases. And life goes on.
Except that now it would be clear that the southern states would not be getting any new slave territory, excpet Texas. And that would be the big issue. Personally I think that before the US can declare war on Mexico again, a bloodier bloody Kansas (which is likely to happen) will result in an earlier civil war.
Mexico for its part has a much stronger north. If it plays its cards right, it will keep this north. California in particular would develop as the highway to the gold rush. My TL bellow is an example of this scenario; where Mexico looses the war, though not as badly as OTL, and emerges as a united and stronger nation.
But if Mexico can't get its shit togeter; if it continues to bicker and the central government refuses to aknowledge the north, then a movement like the Rio Bravo Republic might become more than a ruse to stick it to Sanata Anna and an actual independence movement (and Southern California would likely develop a similar movement). That is up to Mexico, but by the time this is happening the US will likely still be suffering its Civil War. A cool scenario would be a set of independnent Sun Belt Republics (CSA, Texas, Rio Bravo, Southern California) as a buffer between Mexico and the US.