I'm curious if people read into the event too much, or if the two were memorialized together, or if their deaths were use to political ends by some. Basically, what did people make of one of the most patriotic coincidences in American history?
Well firstly, sadness. These men were not just respected by the American public, they were loved. Their deaths prompted mass gatherings in East Coast cities, where people listened to eulogies, and gathered to discuss the lives of these two men.
But, regarding the timing of their deaths, people reacted in various ways. The odds of these events occurring (as what may have prompted this post) is insanely small. Two founding fathers, passing away on the same day is in itself a low-odds event, but the fact that they also died on a national holiday (50th anniversary nonetheless) was pondered upon by the American public, leading to voiced speculation by many public leaders.
As a mostly Christian society, there should be no surprise that a primary public view was that 'divine intervention' was involved in their deaths. Upon hearing the news, John Quincy Adams, (John Adams' son and then-President) wrote in his diary after hearing the news that their deaths were "visible and palpable" manifestations of "Divine Favor". Likewise, in Baltimore, Samuel Smith presented a eulogy, proclaiming that their deaths could be attributed to "All-seeing Providence as a mark of approbation of their well-spent lives".
Another view held by some writers of the time was that they had hung onto life, as to intentionally die on this day. In a NYC eulogy, C. C. Cambreleng said of Jefferson's death: “The body had wasted away—but the energies of a powerful mind, struggling with expiring nature, kept the vital spark alive till the meridian sun shone on our 50th Anniversary—then content to die—the illustrious Jefferson gave to the world his last declaration".
On the other hand, one controversial slice of the public whispered notions of a 'silent conspiracy' among doctors and family members. That Adams and Jefferson were helped to survive until the 4th, and then treatment was either discontinued, or the patient was sabotaged. Although many thought this was far-fetched, there is tangible evidence at least a fraction of the American public did in fact believe this as true. A letter by John Randolph of North Carolina written to a friend suggests that the lives of these men were taken:
"And so old Mr. Adams is dead; on the 4th of July, too, just half a century after our Declaration of Independence; and leaving his son on the throne. This is Euthenasia, indeed. They have killed Mr. Jefferson, too, on the same day, but I don’t believe it."