Here's a start at an answer.
PoD is 1843 or 1844. Former President Martin Van Burn makes a strong run for the Democratic nomination. He never publicly volunteers his personal viewpoint that he is against the annexation of Texas, and without that holding him back, is able to secure the Democratic nomination based on his cultivated political networks and name recognition, preventing the emergence of any dark horse Presidential candidate like James Polk of Tennessee.
Meanwhile, Henry Clay is the nominee of the Whig Party.
Clay wins, advantaged by the salience of economic issues and outside of committed Democratic partisans, memories of Van Buren's association with the Panic of 1837.
Clay, at least in the early years of his term, has a working Whig majority and passes elements of the Whig program, the American system. He declines to annex Texas. Outgoing President Tyler fails to secure a resolution annexing Texas, and seeing it unlikely to succeed in passing Congress, probably does not make the attempt.
While President, Clay also declines to alter the status quo in Oregon, continuing the status quo of Anglo-American condominium, to the dissatisfaction of American expansionists.
However, Clay cannot and does not really seek to squelch internal expansion, and Florida is admitted as a slave state in 1845. This is followed by admission of Iowa as a free state in 1846. With that, parity between free states and slave states in the Union and Senators in the Senate is maintained.
The Democratic Party, unlike the Whigs, is in the main, supportive of expansion both in Texas and Oregon, and seem ready to make an issue of it in their 1848 campaign.
In 1848 Wisconsin is admitted into the Union as a free state, giving the free states a one state, two Senator advantage over the slave states. Meanwhile, for the Presidential election, Henry Clay is lame duck, pre-pledged to not run for a second term by Whig Party ideology. The Whig Party seeks its next nominee, whom I have not figured out yet.
Daniel Webster would likely be a competitor for this nomination but is not assured of winning it.
On the Democratic side, the alarmed reaction of southern Democrats to the admission of Wisconsin and loss of Senate Party, voiced by old John Calhoun in particular, turns the Party's expansionist plank, formerly uniting the Party, into a divisive intra-Party issue. Lewis Cass is the leading northern and western candidate for the President, and favors expansion in both Texas, and possible points beyond in the southwest, and in Oregon, to the parallel 54-40. However, southern Democrats, while supporting Texas annexation and possible additional southwestern annexation, recoil from annexation in Oregon, or certainly annexation of the entire territory to 54-40, or risking war with Britain , their main cotton market, for purposes of annexation. Southern delegates coalesce around a candidate of their own for the Presidency in competition with Cass.
As a result of divisions in Democratic ranks, if nothing else, the Whig nominee carries the electoral college in 1848 and wins the Presidency. Their territorial policy, ultimately, is to refrain from annexation of Texas, but to work out the peaceful division of Oregon along the 49th parallel (less Vancouver island) with Britain.
Meanwhile, in 1848, a Mormon migration to Great Salt Lake in northern Mexico has occurred, and gold is discovered at Sutter's Mill in northern California, leading to to an influx of prospectors and other migrants, from the USA, Mexico, and the world over, to northern California for the rest of 1848, 1849, and into 1850.
The Mexican Republic is unable to control the influx, and newly springing up communities make their own law via vigilance committees. The Mexican government does try to expand its troop and naval presence to the Presidios and to collect revenue, for near non-existent services, which serves to irritate local communities. This serves to provoke a local California Republican revolution likely in 1850, or 1851 at the latest.
The resulting map of the area north of Mexico looks like below.
....ignore how it portrays the US Canada border.
Mexico retains control over the Rio Grande Valley and its traditional settlements of Santa Fe, and southern Alta California, and the deserts and mining districts in between.
The Whig Administration does not entertain any petitioning from the California republic to join the USA, like it has not with Texas. Mexico has not recognized California independence and is still contesting it. And California may not be hungrily petitioning as much as Texas because of its remoteness, the lesser realistic Mexican military threat and California high revenue compared with low debt ratio given its abundant gold strikes. and port revenues.
....and that's all I have for now...