IMO Southerners objected to the Republican party's anti-slavery expansion position not so much because they expected slavery to expand within the current boundaries of the US (which was pretty clearly impossible after Kansas rejected Lecompton) or even because they mecessarily wanted to expand the southern slave system into Latin America--they were actually divided on the feasability and desirability of this. Rather, they objected to it because they considered it a *symptom* of the Republican Party's desire to assure northern control of the federal government, which could then be used for antislavery purposes. William J. Freehling has noted the paradox that the South Carolinians, the most ardent secessionists, were among the most skeptical of territorial expansion. Observing that Calhoun had opposed the drive to acquire All Mexico, Freehling adds:
"Some leading South Carolinians continued to harbor distaste for proposed Caribbean expansion in the 1850s. Mexico seemed full of non-American peons, Cuba full of free blacks, and the Southwest full of coarse frontiersmen. "It is not by bread alone that man liveth," intoned South Carolina's revered Francis Sumter in 1859. "We want some stability in our institutions." 12 South Carolina reactionaries wanted to stabilize their people-—in South Carolina.
"Many South Carolinians opposed a supposedly destabilizing Caribbean empire because they favored a supposedly stabilizing disunion revolution. These disunionists hoped that outside the Union and beyond unsettling northern attacks, a settled South could flourish. They feared that if the Union did acquire vast tropical lands, grateful Southwesterners would never secede and declining Carolinians would never stay east. Still, a taste for staying home and distaste for expansionism swept up the powerful South Carolina Unionist U.S. Senator James Henry Hammond, just as it did the secessionists. "I do not wish," said Hammond, "to remove from my native state and carry a family into the semi-barbarous West."
https://books.google.com/books?id=MOainyyGxhsC&pg=PA168
(FWIW, Confederate diplomats during the ACW tried to reassure the Mexicans: yes, we wanted Mexican territory when we were in the Union--but only to counterbalance the political power of the Yankees. Now that we're out of the Union, we have no need for your territory, and it's the Yankees you should fear. Of course, they would say that, wouldn't they? But it was not *necessarily* entirely false...)
By the way, the fears of the South that blocking slavery expansion was only the first step in the Republicans' antislavery agenda were not totally unfounded, at least so far as the radical wing of the party was concerned. As Eric Foner noted in *Free Soil, Free Labor, Free Men: The Ideology of the Republican Party Before the Civil War*:
"After they joined the Republican party, the radicals did not abandon their program of political action, nor did they seek to conceal that their ultimate objective was complete emancipation. Henry Wilson told a New York audience in 1855 that he favored immediate abolition “wherever [slavery] exists under the Constitution of the United States,” and he told a Michigan convention in the same year that Republicans “mean to place the Government actively and fully on the side of Liberty. . . .” “Let it be distinctly understood,” Wilson declared, “that our object is the emancipation of the bondsmen in America.” The influential western editor John C. Vaughan informed Chase that the “one end” of political anti-slavery was “the best means by Northern action of securing Southern Emancipation. . . .” 40 During the 1856 campaign, Horace Greeley wrote a public letter which candidly acknowledged that preventing the extension of slavery was only “the first practicable step” toward abolition, and that when the Republicans gained power, “other steps will naturally follow from which conservatives will probably recoil.” After the defeat of Fremont, as conservatives sought to moderate Republican platforms in many states, the radicals did not waver in their adherence to their program. The radicals, Chase wrote Giddings in 1857, must insist upon the denationalization of slavery, not mere non-extension, as party policy, “boldly avowing that we expect as the consequence of such action that slavery will be abolished everywhere. . In the same year George Julian chided Republicans who were “ashamed to avow” that abolition was “our ultimate purpose as members of the Republican party,” and in 1858 the Chicago Tribune editorialized that complete abolition was a goal “devoutly to be wished and earnestly to be labored for,” but that the party was committed to “first securing to freedom the new and unoccupied Territories of the Union.” 41 Nor did radicals moderate their program during the presidential year of i860. Charles Sedgwick told the House in March that he wanted the government to go to “the extreme verge of constitutional authority” against slavery, and a former Congressman from Maine, Daniel Somes, declared in October that a Republican victory would lead to abolition in the nation’s capital, an end to the use of slaves in federal employment, and eventually to emancipation in the South itself. 42 All in all, the radicals made it quite plain that they would hardly be satisfied if a Republican government merely prevented slavery from expanding. From first to last, the stakes for which they aimed were far more comprehensive..."
https://archive.org/stream/freesoilfreelabo01fone#page/118