Another POD could be this: If Houston can convince his army to keep retreating (which seemed to be his plan), he may be able to get the Mexican army to follow him to Louisiana. At which case, war with the U.S. becomes likely.
This is a good point. Houston's strategy did seem to hinge on a lot of strategic withdrawal. However, he probably still would have fought San Jacinto. Maybe, we could POD and have Santa Anna recognize the potential trap and retreat from that encounter. But if so, I don't see why Houston would lead him into Louisiana. There's no guarantee that the US will join, given Northern feelings in Congress. Plus, the Sabine River is quite a big river to attempt fording and building rafts/pontoon bridges would have been difficult for Houston to do on the run.
Maybe he leads Santa Anna on such a wild goose chase, nipping at the flanks of the Mexican army and their supply lines, giving more provinces a chance to think about the Dictator's tactics. A more general rebellion in Mexico itself breaks out. Meanwhile Southerners, flush with news of Houston's brilliant campaign, flock across the border in droves. Maybe, just maybe, this becomes part of the Presidential Campaign of 1836. More likely given the necessary time and distances it becomes part of Congressional campaigns in 1837, since that early in the 19th century many states, though mostly Southern ones, held Congressional elections in the odd years preceding the term of a new Congress. This provides some chance for aid to Texas becoming an issue. Again, the North still has no reason to side with the nascent Lone Star Republic. Also, if Houston's tactics are proving successful, Texas may not want annexation, especially since a peace treaty that might emerge from such a campaign might actually leave Texas and Mexico at peace, as opposed to OTL when Santa Anna reneged on a treaty he agreed to at gun point after regaining power in Mexico around 1840.
Also, the main issue isn't Jackson annexing Texas/going to war for Texas, but Van Buren. By the time Jackson could consider annexing the RoT, he's a lame duck and can do little.
Perhaps you need a much earlier POD, with a more lengthy Texas Revolution. But it's still hard to find a casus belli short of outright land hunger that would see the North permit an intervention in a revolt of slave-holders against an abolitionist, central regime.
One final possibility is for Jackson to take matters into his own hands and unilaterally order US military support. I'm not sure if the military would follow such orders. But once he does, how can Congress impeach a lame duck President for starting a war once the enemy pursues the conflict in earnest? This would cause quite a stir, nonetheless, and Northern Congressmen would doubtless seek to limit potential slave holding gains as much as possible. Hence a second war would be necessary to get the rest of the Mexican Cession.
An earlier Texas/Mexican War for the US would advance the debates that caused the Civil War. OTL, the Mexican War was the first time that large scale, American expansion was opposed on the grounds that it would add slave states. Expeditions to liberate/conquer Canada in 1812 hadn't prompted fears of free state domination from the South nor had Jackson's seizure of Florida in 1819 prompted blow back from the North. The North has somewhat less to fear if gains are limited, since a smaller Texas would be hard to break into several slave states. But finding consensus on a second Mexican War might therefore be even harder. Southern Secession, if it occurs, might occur much earlier due to increased tension and feeling that the South has less room under the terms of the Missouri Compromise than the North.