Suppose James K. Polk dies a few years early--say, by early 1844. There are still enough people opposed to Van Buren to block him at the Democratic National Convention, but on the other hand many do not want Lewis Cass, who is seen as too conservative and pro-soft-money. What are the alternatives, apart from James Buchanan--who if elected in 1844 might have a considerably better reputation than in OTL as I noted at
https://groups.google.com/d/msg/soc.history.what-if/4BhecY4CXHs/GiO48iZeCgAJ ?
One idea would be, as in 1852, to try a dark horse from New Hampshire--in 1844 this would be not Pierce but Levi Woodbury. As a Jackson loyalist during the Bank Wars and later a staunch defender of the Independent Treasury, he would be acceptable to the Van Burenite hard money men. And as noted at
http://www.famousamericans.net/leviwoodbury/ he "voted in 1844 for the annexation of Texas" which would make him satisfactory to Southerners.
One other idea: in OTL when it was clear that Van Buren was sinking, the Van Burenites tried to get Silas Wright
https://en.wikipedia.org/wiki/Silas_Wright to run instead, in order to stop Cass. In OTL Wright declined to run, partly because he did not want to profit from his friend Van Buren's defeat, and partly because he thought Polk a good compromise candidate. If there had been no compromise candidate available, might he have changed his mind? No doubt the Texas-above-all faction of the Democrats would not be happy with Wright, but those who used Texas merely as an excuse, and were really more concerned with Van Buren's unpopularity (due to the Whig-inspired image of him as a cold-hearted aristocratic dandy luxuriating in the White House and indifferent to public suffering during the depression) might find Wright more acceptable. In any event, Wright would certainly be the Democrats' strongest candidate in New York, and without New York the Democrats' chances of winning the presidency were fairly bleak.
OTOH I doubt that as a presidential candidate Wright could dodge the Texas issue as he did as a gubernatorial candidate. True, his handling of the issue was adroit for the purpose of putting New York in the Democratic column: Wright merely spoke vaguely about the peaceful and honorable acquisition of Texas and Oregon within a few years (which seems a rather strained interpretation of the Democratic platform's call for the "reoccupation of Oregon and the re-annexation of Texas, at the earliest practicable period"). If he tried to equivocate like that as a presidential candidate, there could be a Tyler third-party pro-Texas candidacy which could doom the Democrats in the South.
All in all, I am by no means certain that Cass could have been stopped if there had been no Polk. After all, on the seventh ballot Cass led Van Buren 123 to 99, and during the adjournment, Richard Johnson withdrew and threw his support to Cass. Van Buren's managers looked desperately for a stop-Cass candidate, and after Wright declined, settled for Polk, who was already being promoted by the Tennessee delegation. I am not sure that Buchanan, Woodbury or anyone else would fulfill that role as well as Polk did. After all, Polk had Jackson's backing, while Buchanan had little support outside Pennsylvania, and Woodbury was from a small state (and one that was safely Democratic in any event) though he would have some support in both New England and the South. And if no strong compromise candidate emerged, and if Cass maintained his momentum, very likely he would either make it to two-thirds, or if he came close to that and seemed to be blocked only by some stubborn hard-core Van Burenites (who would make themselves very unpopular with the rest of the convention), perhaps the convention would reconsider and decide to abandon the two-thirds rule after all, which by that point would guarantee Cass's nomination.