The Annexation of Texas, the Mexican-American War, and the Treaty of Guadalupe-Hidalgo, 1845–1848. During his tenure, U.S. President James K. Polk oversaw the greatest territorial expansion of the United States to date.olk accomplished this through the annexation of Texas in 1845, the negotiation of the Oregon Treaty with Great Britain in 1846, and the conclusion of the Mexican-American War in 1848, which ended with the signing and ratification of the Treaty of Guadalupe-Hidalgo in 1848.