A Two-Term Henry Clay Presidency?

Some time ago, a participant at Civil War Talk asked a "what if" question about a Henry Clay presidency:

How would have the political situation had developed by 1860 with a two-term Clay Administration rather than the a Jackson one, or even more intriguing a Whig dominated two-term Clay Administration in the 40's?

I began by addressing the question, when Clay might have been elected:

Boy, that's a tough "what if." Since it's vaguely relevant, I'll begin by noting that Clay's best chance of winning the presidency probably came in 1840 -- the year he wasn't nominated. The Whigs held their convention in December 1839 and nominated Harrison. There was a brief economic recovery in 1839, and the perception at the time was that Harrison was more electable. In 1840, the economy collapsed again. If the Whigs had held their convention in mid-1840, the Whigs' concerns about electability would have been less, Clay would likely have been nominated and would likely have won. . ..

I raise this to tout Daniel Walker Howe's magnificent new book, What Hath God Wrought: The Transformation of America, 1815-1848 -- and to pat myself on the back. Although Professor Howe does not specifically address whether Henry Clay might have won in some year other than 1840, he certainly endorses the ideas (a) that the timing of the Whig convention was crucial to Clay's failure to secure the Whig nomination that year, and (b) that Clay would probably have won if he had been nominated:

As a Whig presidential victory came to seem inevitable [as the economy continued to worsen during 1840], the significance of the early date of the Whig convention became apparent. Some Whig politicians, particularly in the North, had supported Harrison for prudential reasons but would actually have preferred Henry Clay as the true embodiment of the party's principals. Now it seemed clear that Clay too would have won the election -- and that he would have gained the nomination had the convention been held later when the full impact of the Panic of 1849 had been felt. Clay himself complained bitterly that he had been "always run by my friends when sure to be defeated, and now betrayed for a nomination when I, or any one, would be sure of an election."