No Kansas-Nebraska Act

In 1854, the South had before it a choice of paramount importance. The Black Warrior Affair had inflamed Nationalism across the nation, uniting both North and South against Spain, granting a grand opening for the claiming of Cuba from that declining European power. As an existing Slave territory, and not of interest to Northerners as a prospective place of settlement, the island could've been annexed and made into a new Slave State for the Union. The alternative option, however, was that of the Territory of Kansas; unlike Cuba, it was a target of Northern interest, being suited for farmers from that section of the nation. The South had enough power that she could seek one, but not both.

Historically, the South quite obviously chose wrong. Her politicians, instead of pushing the Cuban angle, instead decided to pick a fight over Kansas via pushing for the Kansas-Nebraska Act, an event which precipitated the collapse of the Whig Party and its replacement with the aggressively Free Soil (with a strong Abolitionist faction to boot as well) Republican Party. Sectional tensions from there on went into a steep decline, ultimately leading to the Civil War. To quote from The Rise and Fall of the American Whig Party by Michael Holt, on pages 981-982:
Further on, in pages 982-983, Holt further states that:
So, what if the South had choose correctly and picked Cuba? Obviously the United States, even in the 1850s, was sufficiently powerful to topple the Spanish authority in Cuba and achieve victory. Nationalist feelings and the previously mentioned characteristics would likely ensure the rapid entry of Cuba as a Slave State into the Union. Without the Kansas-Nebraska debacle, the Whigs would also likely to remain around, helping to keep tensions between the sections of the country in check. More importantly, it would've opened up further opportunities for expansion. According to President Buchanan's Proposed Intervention in Mexico by Howard Lafayette Wilson, from the The American Historical Review Vol. 5, No. 4 (Jul., 1900), pages 687-701:
Reignited antislavery sentiment in the North, spurred on by the Kansas-Nebraska controversy, meant it was impossible for such to make it through Congress. Buchanan would not be deterred, however, and would attempt to get around the Congressional hostility by by negotiating the McLane-Ocampo Treaty. This too failed, and ultimately the President was compelled to give up his schemes. However, given the hypothetical of the Kansas issue being avoided, it is perhaps entirely possibly to see Buchanan having his way on the matter. Most likely this adventurism would result in the establishment of a protectorate over Mexico, ultimately transitioning into full blown annexation; afterall, even historically several regional Mexican strongmen would seek to be added to the United States and, later one, even the Confederacy.