I have to disagree with your belief that Clay was capable of stopping Nullification in South Carolina. South Carolina was finally stopped in March 1833; and Clay’s Compromise tariff wrongly gets a lot of credit for this. Known as the compromise tariff of 1833, many historians believe this is what ended the crisis. This helped, but it only worked with the passage also, of Jackson’s Force Bill, which gave the president the ability to put down insurrections in states. That Jackson as president already had precedent for doing this, and yet still sought congressional approval, is testament to his shrewdness. Further support for this is found in the fact that Jackson had already offered a lower tariff to South Carolina than Clay’s....which they refused. This of course was before the Nullification Proclamation; and this document, with national acclaim it garnered, is a major reason South Carolina finally backed down.....and Henry Clay was most certainly not capable of envisioning the Union as Jackson does in this proclamation.
Also, Jackson’s military background and his notorious hot headed nature (which, as president, this latter characteristic was used for effect more than anything) led many in South Carolina to believe Jackson would come to the Palmetto state with Federal troops. People were afraid of Jackson, and while his correspondence reveals no desire to go down to the state and make war, he certainly made South Carolinians feel it was a possibility.
Jackson’s Nullification Proclamation is what stopped Nullification in 1833; and in 1861, Lincoln will look to this document for inspiration in his struggle. Clay was incapable of concieving of a nation were secession was impossible. Had Clay been President, the federal government at that time would have lost the Nullification debate, and the county would have been much different.
Also, Jackson being a southerner, and a known decentralist, made his beliefs in the Nullification Proclamation easier to believe as genuine all over the country, and made South Carolinians seem small and petty. Adams would have had a harder time because he was a northerner, and very pro-tariff.
All matters of “what if,” since Clay never got close to the White House. I think he was hard-headed enough that he would have done what was necessary.