Three former U.S. presidents from both major political parties made a significant statement this week: They would take a coronavirus vaccine on camera to soothe any public concern.

What we don’t yet know is how much President Trump will do to accomplish the same task. But a new poll shows just how important that might be in the waning days of his presidency. Indeed, it might be the most significant remaining question of the Trump era.

With multiple vaccines in the final stages of approval and hope for their extensive deployment in the weeks and months to come, Trump is preoccupied with a quixotic effort to remain in office. He has in the past hailed the rapid development of vaccines, including holding them out as a potential quick fix during the 2020 election. But since he lost the election, he has shown much more of a desire to claim credit for that development than to focus on the rapidly growing coronavirus problem in the United States, where the daily death toll is now setting records and things are on a terrible trajectory. Trump has also in the past expressed skepticism about vaccines — most notably and baselessly linking them to autism — and flouted some of the more basic coronavirus mitigation efforts, including questioning the efficacy of masks.

A new Pew Research Center poll demonstrates the need for Trump to double down on the vaccine if it is to tackle the problem.

First, the encouraging part: Although the Pew poll in September showed only about half of Americans said they would likely get the vaccine, today that number has risen to 6 in 10. That’s still down from April, when 73 percent said they were likely to get it, but it’s an improvement.

Driving the increase appears to be the reality of the coronavirus situation. While 59 percent of Americans in June said the worst of the coronavirus was yet to come, that number is now 71 percent. The current death toll indicates the worst is pretty much inevitable — if it hasn’t arrived already — but there is at least a rising acknowledgment of that.

In addition, the virus has touched many more people personally in the past several months. In August, 39 percent of people said they knew someone who had died of or been hospitalized by the virus. That number is now a majority: 54 percent.

But significant partisan differences remain when it comes to the vaccine — and, perhaps more important, the seriousness of the threat. While 6 in 10 Americans say they would probably get a coronavirus vaccine, that number is 50 percent for Republicans and Republican-leaning voters. They are also much less concerned about the virus, with 43 percent saying it’s a major threat to U.S. health, compared with 84 percent of Democrats and Democratic-leaning voters. A majority of GOP-leaning voters haven’t regarded the virus as a major threat to public health since early in the outbreak.

In other words, even among Republicans who are open to getting the vaccine, there appears to be less urgency to take such steps. If you don’t view the virus as a major threat — despite at least 274,000 deaths in the United States — you’ll be less motivated to get a vaccine.

(As the 2020 election showed, polls can be off. But when it comes to broader public sentiment, being off by a few points isn’t as significant as in an election where you want to get a sense of an outcome. And Pew’s numbers show how these numbers have shifted over time, using similar samples.)

This is where Trump comes in. He has certainly been an advocate for these vaccines. But as with many aspects of his presidency, it appears to have been self-serving — an effort to pump up his reelection campaign and, perhaps first and foremost, to convince people that we could avoid more restrictive mitigation efforts.

Trump has long been seemingly more concerned about reelection and the economy than about the true threat of the virus, which he has consistently downplayed and suggested would suddenly disappear. Those considerations weigh less heavily on his actions now that the election is over, and his lack of public comment on the virus even amid the current spike — along with his lack of engagement on the topic in recent months — would seem to show where his true priorities lie.

But he will have plenty of influence when it comes to how effective the deployment is. Not only might the vaccine become publicly available in his final weeks in office, but his sway over the GOP base will remain significant for months or years to come. His cheerleading for vaccines thus far hasn’t led to a huge embrace in GOP circles — undoubtedly partly the result of his diminishing of the actual threat — but he could do plenty to persuade some of the most skeptical Americans to get vaccinated, if he chooses to.

And to the extent he decides he doesn’t want to get involved, that will be particularly conspicuous — especially if his three predecessors and others are making such a public show of it. Trump has promoted the vaccines, but degrees of support and emphasis matter. And it’s Trump’s base that needs the most convincing, even as the vaccines are on the doorstep.