Northern position- Northerners were concerned about the annexation of Texas because they did not want the United States to add another slave state. According to the Missouri Compromise of 1820, Texas would enter the Union as a slave state since it is located south of the 36'30 line.
Southern position- Southerners wanted Texas to join the Union. Having Texas added as a new state would mean that people in favor of slavery would have more power in Congress, since each state has representation in both the Senate and House of Representatives.