Not really. It would already have neighbors with expansionist policies that out populate, out produce, and out finance it from the start. It wouldn't have the American starting advantage of having no real neighbors at all, it wouldn't have the Mexican advantage of starting as a single political unit however shakey, and it would have the huge disadvantages of being small and weak with more land than it can possibly control, let alone guard.
Plus, as I mentioned before the main heart of their economies would be still born. The US, Britain, and Mexico can swamp its markets with goods, they wouldn't enjoy the common-market/cheaper defense of being part either larger nation, the Californian economy would be kicked in the nadgers without the plentiful electricity of Washington, and there's no real resource in this union that isn't more common in the US or Mexico. Short of going into vassalage for another power, I'd give it a decade or three on the far end.
Gold in CA starts something going there. Oil in Texas in the same way. There's the hydroelectrics of the Hoover Dam. The agricultural wealth of the Imperial Valley and the Rio Grande Valley, which have year long growing seasons. There's a chance. It's incredibly shaky, but it's there.
Also, any scenario which sees TX or CA indepedent does so because the US loses its expansionist fervor. Which wasn't much of a fervor, since large sections of the country opposed the acquition of territory detrimental to their own interetests. Politics changes in some way (Jackson is killed at New Orleans, for example), and Manifest Destiny doesn't take hold or abolitionists take a stronger stance.
Britain was perfectly happy to invest in the USA and the USA perfectly happy to take the capital, despite the tarrif wall. If the RoT lacks the tarrif, which it probably would, then Britain might invest more readily there. Lack of the same constitutional restrictions and geography would make transcontinental rail far easier and quicker to build in the RoT than in the USA. If the US fights a Civil War, without which its own internal development will be dampened by more strict federalism, Texas has a decade to develop in blessed neutrality, and attract further immigrants.
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