POD: Martin Van Buren wins the Democratic nomination after he agrees to support Texas annexation.
Van Buren/Polk win the general election.
Van Buren negotiates the peaceful annexation of Texas with Mexico in 1845.
A few years later, the Mexican government needs money and agrees to sell a large chunk of territory (N California, Nevada, Utah, and Colorado) to the US in 1848. All this territory is north of the Missouri Compromise line and is therefore free territory.
No Mexican War would mean no dress-rehearsal for the Civil War.
1848: Polk/Pierce wins the over Clay/Fillmore.
1850: Polk dies in office and Vice President Franklin Pierce becomes the 13th President.
1852: Pierce/King wins over Scott/Graham.
1854-1864: Pretty much the same as OTL.
1865: Mexico agrees to sell the US the rest of California (including Baja) and New Mexico.
It might also alter national boundaries a bit. California might be divided at the Tehachapi mountains (LA and possibly Las Vegas remain in Mexican hands) while New Mexico might not include what later became the Confederate Territory of Arizona (adios Phoenix and Tuscon). As for the Civil War it depends on how the territory gets divided and whether William Walker et al can succeed in filibusters later on. As for Mexico this will further fragment the government and might prevent them from retaking the Yucatan at all. There were two or three other provinces seeking their own way as well and without the Mexican American War I am unsure if Mexico as we recognize it survives.
You'd probably get borders really similar to what Herrera proposed right before he was kicked out.
Tamaulipas keeps the Nueces Strip and Coahuila the Pecos. So the Texas border follows the Nueces River to the Pecos River and from there up to the 37th parallel and a straight line to the Pacific, this keeps most of the populated areas of New Mexico in Mexico all of present day Arizona and California South of Monterrey Bay.
If that seems to far North probably the most the US can get without a War could place the border at the 35th parallel rather than 37th.