I doubt that Calhoun could finish in the top three. It's not as though he is going to sweep the South, with three other southern slaveholders (Jackson, Crawford, Clay) in the race. (Even in South Carolina, Calhoun's support was not unanimous; there was a pro-Crawford faction led by Senator William Smith.) In the North, Calhoun's big hope was Pennsylvania (where voters were perhaps not yet aware of the extent to which he was abandoning his earlier nationalism and pro-tariff views), but that faded once Jackson became a candidate. George M. Dallas, Calhoun's most ardent supporter in Pennsylvania, warned him early in 1824 that he might be defeated there because of Jackson's sudden entry into the race. Sure enough, at a meeting of local delegates at Harrisburg on February 18, Jackson was unanimously nominated for president; Dallas himself bowed to the inevitable by offering the resolution nominating Jackson.
"On March 4, the Pennsylvania state convention repeated the action taken by the Harrisburg delegates, but instead of eliminating Calhoun altogether the convention nominated him for the vice presidency, an action later imitated by Maryland, New Jersey, and North and South Carolina. Although his abrupt removal from presidential contention came as a shock, Calhoun was enough of a realist to accept the verdict as final and for the moment set aside his presidential ambitions. With this shift of strategy, he suddenly found himself the only national candidate for second place. The friends of Adams also awarded him their support and so, in a sense, the South Carolinian became the running mate of two presidential candidates." Robert Remini, *Andrew Jackson and the Course of American Freedom 1822-1832*, pp. 65-66.
https://books.google.com/books?id=kbM-AAAAQBAJ&pg=PA65
The basic problem is that outside South Carolina most voters who liked Calhoun liked Jackson more. So Calhoun's settling for the vice-presidential nomination was probably the only realistic course he could take. One should also remember that Calhoun was young for a presidential candidate--only 42. In fact, I'm not sure whether he would have run for president so early (instead of waiting four years) if not for the fact that he detested Crawford (who was certain to get the endorsement of the Congressional Democratic-Republican Caucus) and thought that Adams was too weak a candidate to defeat Crawford. Once Jackson entered the race, that particular reason for a Calhoun candidacy faded, since there was now a strong anti-Crawford candidate. Finallly, Calhoun lacked one of Jackson's great advantages (even apart from military heroism): Jackson was running as the "outsider", protesting the alleged corruption and waste in the Monroe administration. Although Crawford was the candidate most vulnerable to this appeal, Calhoun had his own vulnerabilities. One was the massive cost overruns on the Yellowstone Expedition, as I explain at
https://groups.google.com/d/msg/soc.history.what-if/VULWYJQEVJo/0s4Kx-7_IngJ
If Calhoun did insist on staying in the presidential race--and made it clear he would not accept the vice-presidency--I am not sure who the Jacksonians would support for vice-president. De Witt Clinton was a Jackson ally and the great rival of New York's leading Crawford supporter, Van Buren. But southerners suspected Clinton of antislavery sentiments. I am also not sure who the Adams and Clay supporters would back--in spite of Calhoun being the official Adams (as well as Jackson) running mate in OTL, some Adams electors (as well as the majority of Clay electors) voted for Nathan Sanford of New York.
http://en.wikipedia.org/wiki/Nathan_Sanford Finally. the "Radicals" (Crawford supporters) originally supported Albert Gallatin for vice-president, but Gallatin proved unpopular (due partly, I believe, to his foreign birth), was asked to withdraw, and gladly did so. Some of the Radicals voted for Macon for vice-president, others for Van Buren, a scattering for other candidates. If Sanford could get some Jacksonian support, in addition to his support from Adams and Clay men, he would certainly be the favorite.