Actually we had disputed border with Mexico due to the Texas rebellion and the fact that Mexico wouldn't recognize the independent Republic of Texas and its boundaries. From Wikipedia:

"After its independence in 1821 and brief experiment with monarchy, Mexico became a republic in 1824. It was characterized by considerable instability, leaving it ill-prepared for conflict when war broke out in 1846.[7] Native American raids in Mexico's sparsely settled north in the decades preceding the war prompted the Mexican government to sponsor migration from the U.S. to the Mexican province of Texas to create a buffer. However, Texans from both countries revolted against the Mexican government in the 1836 Texas Revolution, creating a republic not recognized by Mexico, which still claimed it as part of its national territory. In 1845, Texas agreed to an offer of annexation by the U.S. Congress, and became the 28th state...."