I'd imagine the most significant scenario is the one that they actually attempted: political officials without medical or scientific expertise attempting to reduce the FDA's safety standards required for authorization of the vaccines.
First, some background context around why these fears existed, which I believe go beyond vague handwaving concerns and are fairly concrete causes why one might have believed President Trump may not be trustworthy if he was involved in decisions about COVID vaccines:
- In the past, Trump made a variety of false claims, not backed by medical experts, about vaccines causing autism
- Trump publicly announced he was personally taking hydroxychloroquine to prevent COVID-19 amid significant safety concerns for those taking the drug. Even after further studies determined it was ineffective, potentially harmful, its emergency authorization was revoked by the FDA, and the WHO announced it was pulling it from a study of potential treatments, he shared a video that claimed the drug was "a cure for COVID" and "you don't need a mask."
- Trump publicly asked health experts at a press conference whether UV light or disinfectants could be injected or otherwise used internally to kill the virus.
- In July 2020, Trump reportedly received briefings, including from pillow salesman and now-election conspiracist Mike Lindell about the use of oleandrin as a COVID treatment, resulting in Trump "expressing his enthusiasm for the FDA to approve oleandrin" despite safety concerns and the complete absence of public studies "showing oleandrin has ever been tested in animals or humans for its efficacy against COVID-19."
- Before Election Day 2020, Trump repeatedly made statements about the availability of vaccines prior to the election. In an October 22 debate, he claimed the vaccine was "ready" and would be announced "within weeks" (and later waffled on that and gave incorrect information when pressed for clarification), and at a campaign rally, said that vaccines would come "momentarily." In September 2020, he hinted at a vaccine before the election, saying "We’re going to have a vaccine very soon, maybe even before a very special date. You know what date I’m talking about." This came even as top health officials, including Drs. Slaoui, Fauci, and Adams, all cast significant doubt on whether trials would be completed by that date. Another September 2020 statement involved Trump saying "We remain on track to deliver a vaccine before the end of the year, and maybe even before November 1. We think we can probably have it sometime during the month of October."
- Perhaps most importantly, President Trump suggested in August 2020 he was dealing with a "deep state" that might seek to delay vaccines until after the election: "And you're going to be hearing some very good news very, very soon. Now, we're dealing with the deep state. So I'm watching it very closely. I don't need to have them announce on November 4th, 'Ladies and gentlemen, we've found the vaccine, it's perfect.' I don't need that. And hopefully everyone's looking to do the right thing."
- He expressed similar sentiments in a tweet: "The deep state, or whoever, over at the FDA is making it very difficult for drug companies to get people in order to test the vaccines and therapeutics. Obviously, they are hoping to delay the answer until after November 3rd. Must focus on speed, and saving lives!"
- The entire situation was nicely summed up by this headline from August 2020: Trump has launched an all-out attack on the FDA. Will its scientific integrity survive?. Or as the New York Times wrote around the same time: "Many medical experts — including members of his own staff — worry about whether Dr. Hahn has the fortitude and political savvy to protect the scientific integrity of the F.D.A. from Mr. Trump."
And so by August 2020, we could say Covid-19 Vaccine Push Lacks a Key Ingredient: Trust. The President had demonstrated a disturbing lack of basic knowledge about medicine, promoted unproven and harmful treatments against medical advice, repeatedly promised vaccines before Election Day, and repeatedly suggested government officials were hoping to delay the authorization of vaccines in an attempt to sabotage his political chances and that he would encourage them to hurry as a result.
And these events occurred around the same time that two vaccine trials were temporarily halted so that independent monitoring boards could determine whether serious adverse events were caused by the vaccines (the trials were subsequently resumed after the FDA gave the OK). This further underscored the need for careful safety testing and for safety decisions to be made without political interference.
All of which is to say, there were specific reasons well beyond partisanship why there were concerns about the scientific integrity of the vaccine authorization process. At this time, and perhaps because of all this, public confidence in the not-yet-delivered vaccines fell significantly: in May 2020, 72% of adults said they probably or definitely would get a vaccine; that fell to 51% by September 2020 (a similar pattern was present for both Democrats and Republicans). I'd have to presume this dramatic drop was part of the motivation for these vaccine panels: to attempt to boost public confidence by offering further independent review of the vaccines.
As for the specific scenario feared, I'd look to what actually happened:
- FDA scientific staff prepared guidelines for their review of vaccines. These included "the recommendation that volunteers who have participated in vaccine clinical trials be followed for a median of two months after the final dose."
- These guidelines were submitted to the Office of Management and Budget on September 21. Two days later, White House Chief of Staff Mark Meadows (who holds no medical or scientific credentials) "questioned the need for two months of follow-up data, said that stricter recommendations would change the rules in the middle of clinical trials and suggested that Dr. Hahn was overly influenced by his agency’s career scientists."
- That same day, Trump said the White House "may or may not" approve the guidelines, and called them "a political move." This came just hours after four doctors leading the government response publicly endorsed the guidelines.
- Even after FDA officials provided information justifying the guidelines, the White House continued to block them.
- On October 6th, the FDA published the guidelines on their website, sticking to their judgement that trial participants be followed for at least two months.
- On December 1, FDA Comissioner Hahn was "summoned to the White House by Trump’s chief of staff Mark Meadows". The Associated Press reported that "as he has refused to accept his loss, Trump also has told close confidants that he believes the vaccine is still being slow-walked in a bid to undermine his efforts to challenge the results. If the vaccine were shipped out sooner, he has argued, it would rally public opinion to his side."
- On December 12th, the FDA authorized the Pfizer/BioNTech vaccine for those 16+. The authorization reportedly only came "after White House Chief of Staff Mark Meadows on Friday told FDA commissioner Stephen Hahn to be prepared to submit his resignation if the agency did not clear the vaccine by day’s end." (The FDA planned to announce the authorization the next morning anyway, and so this pressure had no real effect.)
All of this is a long way of saying that:
- The President had a track record of pushing for and promoting untested and dangerous treatments against the advice of experts.
- The President repeatedly promised vaccines before the election and suggested that "deep state" government scientists were delaying vaccines to hurt him politically.
- White House officials attempted to override the judgement of FDA scientists about the extent of the trials needed to ensure vaccine safety.
- The President believed that authorization of the vaccines could help his chances of overturning the election results.
- White House officials threatened the FDA Commissioner's job if a vaccine wasn't authorized immediately.