IC: The US gets free access to the oil that was discovered in Texas in 1937. If you want to use the Dragonfly Effect(1), you could alter that date by about ten years either way.
You might have Mexico get slapped down by the US when it's internal problems can't be contained on the Mexican side of the border, rather than having the latest Mexico-Texas grudge-match light off a general war among all of the 'American Powers' that needs the intervention of the Empire to put a stop to the madness.
With Texas and the '*Allied States'(2) still in the Union, the Yanks might not get sucked into the 'Collectivist Wars'(3) of the mid-to-late 20th Century. Hell, Collectivism as an ideology might just be 'Dragonflied' away. Along with such other vile beliefs as 'Falangism'(4) and 'Chauvinism'(5).
OOC: The 20th century was pretty much inevitably going to be a time of turmoil, it was just a matter of when all hell broke loose, not if it was even going to in the first place. technology lagged behind ours until the big wars in the middle of the century, and still are behind in some areas, (transportation is a good example, this world's latest jet aircraft would not have been out of place in the 1970s in our world, rocketry is where we were in the mid 1960s at present), but are way ahead in others, such as medicine and communications. (Apart from satellites, which they are only developing. Everything is currently run over fiber optic cables, and better than two in three own a cell-phone, even if they call one by a different name.)
1. For an alt-butterfly effect, one can substitute just about ay flashy flying creature, so it could just as easily be called the 'Hummingbird Effect'. Using analogy like that is a simple and effective way to explain chaos theory and how a small change can have enormous effects.
2. An Alt-CSA, doesn't include Texas, (obviously), Virginia or Kentucky. gained independence via a referendum following a short, inconclusive war. Lincoln came to power in the US on a platform of preventing any other state from seceding. Jeff Davis was Lincoln's successor as president, elected in 1872.
3. Alt 'World Wars', first one was from 1947-55, second was from 1966-70, and the third was from 1991-1993, nuclear weapons came in 1969, and ICBM type weapons came in 1993. For an idea of what the last one would be like, the combat scenes in 'Red Storm Rising' would be an accurate description, until the nuclear missile bit, that is. For that, 'The Day After' would be a good example, but the barrage would be completely one sided. Collectivism itself is an Alt-Communist type 'people's dictatorship', with an economy more or less on the lines of present day China. The ideology is also called Marxism, though both the alt-Marx and the real one would be appalled to see it. The last traces of this toxic ideology were scourged away by a massive bombardment of nuclear weapons in 1993.
4. Alt-Fascism. As in Italian style, complete with a Mussolini type dictator in charge. IOTL Falangism was the name given to Spanish, Portuguese, and Latin American versions of fascism. Here Fascism first arose in Spain, and apart from it's nasty, racist, French variant, has never been completely discredited, sort of like some forms of communism IOTL.
5. Alt-Nazis. French alt-Nazis. With a Napoleon complex to boot. managed to pull off an (admittedly unsuccessful) invasion of Great Britain before being crushed under the weight of both the British Empire and the Americans. (Who seriously resented having their trade disrupted by foreigners.) Managed to conquer most of non-Russian Europe before being crushed under a weight of numbers in 1970. With Europe then being split between what was under British control and what was conquered by Turkish (of all things) collectivists forces.