WI: USS Princeton Disaster kills President John Tyler?

On February 28th, 1844, the USS Princeton sailed down the Potomac River on a pleasure crew, carrying President John Tyler, his cabinet, Former First Lady Dolley Madison and four hundred other guests, during a demonstration of one of the ships guns, there was a malfunction and the gun exploded; sending shrapnel everywhere and killing among others, Secretary of State Upshur and Secretary of the Treasury Gilmer; but not the President.

What if this explosion had killed the President? this would mean that President Pro Tempore Willie Person Mangum would succeed to the office (due to the absence of a Vice President); how would this change history?
 
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