Final answer:
The United States was concerned that annexing Texas would lead to political tensions with Mexico and potentially a war, coupled with the problem of slavery expansion which could upset the balance between slave and free states.
Step-by-step explanation:
One of the main issues concerning Texas that worried the United States before annexation was the prospect of inflaming political tensions with Mexico. Annexation appeared imminent due to the push from American expansionists and settlers, especially those profiting from the availability of land in Texas. However, there was a strong concern that such a move would lead to war with Mexico, as the region was still regarded by Mexico as part of its territory despite Texas's independent status as the Lone Star Republic. Adding to these tensions was the problem of slavery, as annexing Texas would mean adding more slave territory to the United States, angering abolitionists and potentially disrupting the balance between free and slave states.