Whigs were opposed to Presidents serving two terms:
"Resolved, That these principles may be summed as comprising, a well-regulated currency; a tariff for revenue to defray the necessary expenses of the government, and discriminating with special reference to the protection of the domestic labor of the country; the distribution of the proceeds of the sales of the public lands; a single term for the presidency;"
That's the 1844 Whig Platform. If Mangum declares himself a candidate in 1844, many will argue that this contradicts Whig principles as he has already served one term. Whigs would already be mad at Mangum for assuming the Presidency itself and not becoming an Acting President instead, as they wanted Tyler to do. I think Clay might have enough support at the convention to overcome Mangum if the latter runs, look at Scott's victory over Fillmore in 1852.