Easy. William Henry Harrison doesn't catch pneumonia. The Whigs get to enact their program, which is successful. Henry Clay wins the election of 1844. The U.S. doesn't annex Texas, there is no Mexican War. Webster wins in 1848. After the Irish Famine and 1848 revolutions start to increase immigration, the Whigs enact restrictions.
Mormons move to Utah in 1846. They remain outside the U.S., forming the Republic of Deseret.
Texas, threatened by resurgent Mexico, allies with Britain in 1847, becoming financially entangled. Texas agrees to abolish slavery eventually in return for British protection and financing. German and Irish immigrants barred from the U.S. start to fill up Texas.
Gold is discovered in California in 1850. There is a flood of immigrant miners, including many Irish, but fewer Americans. In 1854, the immigrants rebel against the Californio oligarchy and declare the Republic of California. Britain supports the rebellion. Alt-California excludes the Los Angeles-San Diego area and the deserts out to the Colorado, but includes western Nevada. The U.S. recognizes California in 1857.
Deseret forms in Utah north of the Colorado, eastern Nevada, Arizona north of the Grand Canyon, Colorado north of the Colorado and west of the Continental divide, and a bit of Wyoming. There's SFA Mexico can do about it.
The U.S. considers invading and subjugating Deseret, but the disunion crisis over slavery pre-empts any action till 1870 or so. By that time Deseret is well dug-in on its territory. U.S. Army commanders on the frontier have established cooperation with Deseret against outlaws and Indian raiders. California recognizes Deseret in 1861. Britain follows suit in 1862. The U.S. finally yields in 1877.