"We have discussed all sorts of scenarios for Henry Clay to become President--1824 (if only he had gotten enough electoral votes to be eligible for consideration by the House), 1832 (very unlikely, especially with the Anti-Masons splitting the anti-Jackson vote), 1840 (had the 1839 Whig national convention selected him), 1844 of course (did Clay hedge too much on Texas? did the Liberty Party vote cost him New York? would a stronger running mate than Frelinghuysen have made a difference? what if Silas Wright didn't agree to run for governor of New York? what if fewer foreigners had been illegally naturalized in time for the election? etc.), and even 1848 (when, if Clay had gotten the nomination, Van Buren's third party candidacy would almost have guaranteed Clay the New York electoral votes he had so narrowly lost in 1844).
"However, there is one other scenario, which would involve Clay becoming President without having won a single electoral vote. It relates to the few months in 1813 when both President Madison and Vice-President Gerry had serious health problems, and there was no President Pro Tempore of the Senate, leaving Clay (as Speaker of the House) next in the line of succession after Gerry..."
http://soc.history.what-if.narkive.com/XESXkPDv/president-henry-clay-181