Actually, the problem of African American slaves escaping into Mexico gave some concern to the US government for decades:
"American acquisition of Florida erased an international boundary that had long been attractive to fugitives, but in Louisiana, slaves could still flee across the Sabine River into Mexico. During the administration of John Quincy Adams, the federal government moved to close that line of escape. The American minister to Mexico, Joel R. Poinsett, negotiated a commercial treaty, and, under instructions from Secretary of State Henry Clay, he secured the inclusion of an article providing for the mutual return of fugitive slaves. Since Mexico had scarcely any slaves except those that Americans were beginning to bring into Texas, this would have been an arrangement beneficial only to American slaveholders on both sides of the border. Some Mexican officials raised objections to the article, but acquiesced when Poinsett insisted in "very strong language" that it was indispensable. In May of 1828, the United States Senate approved the treaty without a dissenting vote and without any discussion of the fugitive slave provision. But in Mexico, both houses of the national legislature rejected the article. 'It would be most extraordinary,' ran one statement, 'that in a treaty between two free republics slavery should be encouraged by obliging ours to deliver up fugitive slaves to their merciless and barbarous masters.' Not until several years later was a redrafted commercial treaty ratified by both nations. It contained no mention of fugitive slaves.
"After the annexation of Texas and its admission to the Union as a slaveholding state, followed by the American victory in the war with Mexico, the problem of international escapes from slavery shifted southwestward to the new international border at the Rio Grande. In 1855, an Austin editor asserted that about four thousand runaway slaves had found sanctuary in northern Mexico. Senator Sam Houston and other Texan leaders repeatedly called the problem to the attention of federal authorities, urging a diplomatic solution before Texans took matters into their own hands. The United States government was responsive. First, Secretary of State John M. Clayton, then the American minister to Mexico, James Gadsden, and then Gadsden's successor, John Forsyth, sought an extradition treaty with Mexico that would include the return of runaway slaves, but all their negotiations failed. Forsyth reported that he could make no headway against 'the British borrowed cant of philanthropy about slavery.'..." *The Slaveholding Republic: An Account of the United States Government's Relations to Slavery,* by the late Don E. Fehrenbacher, completed and Edited by Ward M. McAfee
https://books.google.com/books?id=tY8_W36yZCwC&pg=PA101
Of course the obvious problem with organizing an Undergound Railroad in Texas is that there were a lot fewer abolitionists to help the fugitives than in, say, the Old Northwest. (Even there, the extent of white abolitionist help has been exaggerated; fugitives were more likely to have been helped by fellow African Americans.) Even so, some slaves did manage to escape to Mexico.
