It's an interesting question, completely an opinion, but I'll give it a try.
All three had predominantly regional interests. John Calhoun's for the south, was responsible for the Nullification Manifesto in 1829, in all likelihood. President Jackson certainly believed he was, even though Calhoun was his Vice President, and said that if South Carolina seceded, he would start hanging nullifiers from the highest tree in the neighborhood, and he might start with the Vice President.
Clay was a westerner, born in Virginia but made his home near Lexington Kentucky. He is known as the great compromiser, mostly for the compromise of 1850, but he is also responsible for working out a compromise that got Missouri to remove the clause in their constitution which forbad the importation of abolitionist literature and the emigration of abolitionists to their state. Without this second Missouri compromise, that issue would have gone on for months. Let's talk about the 1850 compromise. Everyone knows that the new Fugitive Slave Law was a part of that raft of legislation, but it also included the introduction of allowing the eligible voters in the territories of New Mexico, Nevada and Utah to choose whether their territories would be slave or free. This popular sovereignty set a precedent that Stephen Douglas followed four years later with the Kansas Nebraska Act, and was the issue that lead to what we know as "Bleeding Kansas". Kansas was kind of a proving ground for the War, and brought men like Ossawattamie John Brown to prominence.
These two features of the compromise were essential building blocks to the war.
Clay was our Secretary of State under John Quincy Adams, and was involved in our early support for Latin American independence movements. The job, then seen as the last step to the Presidency (4 of our 6 Presidents has held the office before being elected Chief Magistrate), came to him as a result of a "corrupt bargain" according to Jackson, as the allegations of immoral conduct were leveled against Rachel Jackson. The editor who had started it all, was a close friend of Speaker Henry Clay, and it's quiite likely that Clay did support this effort, but there is no real quid pro quo to show that the vote in the House of Representatives was rigged. There were four candidates who divided the votes of the electoral college, but none had more than one half of the entire college. William Crawford suffered a major stroke before the vote came to Congress, and wasn't included. The actual vote was between Clay, Jackson, who had the majorit of the popular vote, first time the popular votes were counted nationally in 1824, and John Quincy Adams. When the election went to Adams, and Clay was named his Secretary of State, Jackson claimed a deal had been made, and the campaign of 1828 began from then.
Webster was a great speaker, though what he actually said is not really known. According to Robert Remini, he would edit his speeches for publication and submit those copies to the newspapers for publication. He probably said substantially what was printed, but he also was able to "tweak" his work later for publication. He started out as a Federalist, and even was present, briefly, at the Hartford Convention which opponents claimed called for New England to secede from the Union during the war of 1812. Webster claimed, and argued fervently, that no such measure was introduced. The measure, he said, came far short of that. As it was, his argument wasn't convincing enough for the general public, and the Federalist party was pretty much gone thereafter. We became a one party nation then, all Republican as they called themselves, though history calls them the Democratic Republicans. They later divided, and became the National Republicans, and the Democrats. The National Republicans called themselves Whigs, after the opposition party to the Tories in the Revolution. The Democrats, and not nearly enough credit for creation of that party goes to Martin Van Buren than he deserves, united in 1824 behind the Hero of New Orleans, Andrew Jackson.
Webster served as our Secretary of State, under Fillmore, well Taylor then Fillmore, the General dying after only about a year in office. I think Webster was the only one to remain in the Cabinet after the General's death, when Fillmore refused to support the Compromise of 1850. It had been all sewn up with the General, but his VP didn't go along with it.
My personal opinion is that Clay would have had the greatest impact overall, but then, as an Illinoisan, I'm a westerner too.