You need to look to the US presidential election in the early 1840s. Details begin to haemorage away from my brain, but the gist is that both probable candidates for the major parties agreed that Texan annexation and the acquisition of new lands from Mexico would split the Union over slavery. They thus agreed to oppose both. Unfortunately for this idea, one of the leading candidates lost the primaries to Polk who pursused the expansionist agenda. Now, if (I think it was Clay ?) had become president instead, had NOT supported Texan independence etc... Texas under Anson Jones was seeking a recognition of independence from Mexico backed by Britain and France; given a decade or so, its quite possible that with the US not interested this will come to pass for Texas. This in itself draws some of the fire from the future potential for a blow-up. Also, without the New Mexico territories the issue of California may well not blow-up in the late 1840s. One might see Deseret being more of a problem, since it is being established in the New Mexico MEXICAN badlands.
Knock-on effects are important here. For example, without the Mexican War there is no payment to Mexico by the USA and thus there is no way for Mexico to basically pay off the Yucatecan leadership and in effect buy back that secessionist province. Thus, Yucatan's offer of sovereignty/suzerainty to other powers would remain valid. I could see a US administration being, paradoxically, interested. Its a stepping stone in the Caribbean, it is expansionism, and it is a distraction. One could see the US getting involved. Or one might not. These things tend to twist and turn in the wind.
One thing that is certain is that during this non-ACW period, the USA is going to be doing SOMETHING. Its not going to be sitting there doing nothing. Thus, involvement in the United Provinces of Central America, possible conflict with Spain over Cuba, possible conflict with Britain over Oregon etc.
Grey Wolf