So I'm looking through A People's History of the Civil War, and it looks like Kendi might be elliding two different things, namely support for secession and support for the Confederate war effort among Southern whites.

From what I can see, Williams is specifically talking about the former (while also detailing many examples of resistance to the Confederate war effort among Southern whites at different stages of the war). Specifically I came across this passage:

"In his seminal study of the secession crisis, David Potter looked at the popular vote for state secesssion conventions throughout the South and concluded:

• At no time during the winter of 1860-1861 was secession desired by a majority of the slave states... Furthermore, secession was not basically desired even by a majority in the lower South, and the secessionists succeeded less because of the intrinsic popularity of their program than by their extreme skill with which they utilized an emergency psychology, the promptness with which they invoked unilateral action by individual states, and the firmness with which they refused to submit the question of secession to popular referenda."

With the footnote:

"Potter, Lincoln and His Party in the Secession Crisis, 208. Potter's conclusions are supported by Paul Escott's more recent study, After Secession: Jefferson Davis and the Failure of Confederate Nationalism, 23-28, 42-44."

Potter's book is from 1942, and Escott's is from 1978. I can't get a copy of Potter, but I did manage to get a copy of Escott. The first chunk of pages very specifically talks about 1860, noting that in the 11 future Confederate states 53.1 of voters in the 1860 election voted for unionist candidates, while 46.9 percent voted for the Southern Democratic candidate Breckinridge, and not all of those votes were tacit votes for secession. It also notes that secession was initially presented by its proponents in 1860 less as an irrevocable step but more as a tactical means of applying pressure on the federal government to negotiate. Escott emphasizes that there was much reluctance and ambiguity in supporting secession, and where there were votes for secession conventions, turnout was much lower than in the 1860 election (e.g. Alabama was 75% of the 1860 Presidential turnout, Mississippi was 60%). Arkansas, North Carolina, Tennessee and Virginia had strong pro-Unionist majorities - at this time.

This changed with the firing on Fort Sumter and Lincoln's April 15, 1861 call for 75,000 volunteers to put down rebellion. The Upper South states basically had to finally come off the fence and pick a side, and rather strongly sided with secession and joining the Confederacy. Escott notes on page 44:

"These events broke a long season of tension and uncertainty in the South. A wave of excitement and enthusiasm replaced the hesitation which had gone before as men welcomed the prospect of action. During the secession crisis, many southern leaders had boasted that any war with the North would be brief and victorious. Encouraged by these predictions, southerners prepared for war."

So I am very much reading these sources, Williams and Escott at least, as saying that a majority of white Southerners did not actively support secession during the secession crisis of December 1860 to April 1861, but not necessarily during the Civil War itself (and we don't have public opinion surveys from that time in any case). Escott's book mostly makes the argument that while Southern whites did eventually turn against the Confederate cause in the war, it was because of military defeat, crushing burdens of the war, and failures of Jefferson Davis' government, and was a turn away out of "despair", rather than out of a sense of antiwar or anti-Confederate activism.

It's definitely true that Unionists, including Lincoln at least until June 1861, believed at the time that there was a "silent majority" of Unionists in Southern states. James McPherson in Battle Cry of Freedom, also citing Potter, notes this, but also cautions against a "misunderstanding of Southern unionism". He notes that this unionism (or "cooperationism") was very much conditional, noting, for example, cooperationists in Alabama who urged the North to not "misconstrue" this support: "We scorn the Black Republicans ... The State of Alabama cannot and will not submit to the administration of Lincoln ... We intend to resist ... but our resistance is based upon the unity of action with other slave states." McPherson notes that most of those elected to secession conventions who opposed immediate secession were in this camp ("It was a weak base on which to build a faith in southern unionism").

One thing further I would note is that Williams' work is part of a series in which Howard Zinn is senior editor (and was a mentor to Williams). I do see some evidence of Zinn's influence, namely in places were Williams discusses how business ties with the South prompted Northern "corporate bosses" and "business elites" with economic ties to the South to push for war to prevent secession. This seems to be, to say the least, a bit of a weak and controversial claim, especially considering that much of New York City (which did heavy business with the South) was vehemently against the Union war effort, to the point of proposals being presented for the city to secede in order to maintain its role in the Southern cotton trade. For whatever it's worth, I'm very skeptical of "the war was only desired by elites and ordinary people didn't want war" argument that Zinn in particular argues for in Peoples History of the United States. It's definitely true that no one wanted a war lasting from 1861 to 1865. It's also probably true that very few actually wanted a war in late 1860. But events moved quickly and radically changed ordinary people's opinions. While there was always gripes about the "rich man's war, poor man's fight", clearly hundreds of thousands, if not millions, on either side, actively participated in the war effort and believed in their respective causes.

So - there are some points made that in their specific claims are definitely widely accepted: support for secessionist convention candidates in 1860-1861 was not even as enthusiastic as the support for the Breckinridge candidacy, and secession was supported by at best thin local majorities of voters. But this is before the actual outbreak of hostilities in 1861, and at that time there was a large support for the Confederate war effort, albeit one that would increasingly wane as the war ultimately turned against the Confederacy.

I don't have that book, but I do have Williams' Bitterly Divided: The South's Inner Civil which if anything is a bit more focused on just this topic, as the title might suggest. I think the important thing to emphasis here is that Kendi isn't incorrect, but I would say he is simplifying (it is, after all, a short remark in an interview not about this topic, so that is basically fine).

Modern opinion polling didn't exist in the 1860s, but yes, if you polled the Southern population in late 1860, secession likely wouldn't have been the popular choice. Especially in the Upper South and the Appalachian regions, I would even say it wasn't even that small a split. The South as a whole was incredibly wary of Lincoln's election and decidedly negative in their assumptions about what it portended, but the loud calls for secession were a product of white elites, and as the first states began to secede, such as in South Carolina, they were the driving force behind it. Secession was not a ballot issue most of the time, and this older answer of mine I would point to as illustration of how in the places there was some sort of popular vote, things were far from clear-cut in favor.

As noted in the linked answer, Georgia was a narrow thin margin and recent study suggests secession lost but the vote was doctored in favor. Likewise Tennessee had a large preference toward Unionists in their vote for delegates to represent them on the issue. But Tennessee is a great illustration of how things changed. Secession was not the preferred outcome for many Tennesseeans in February, but in June secession passed with overwhelming support. The changes of the previous few months saw a large shift. More states seceded, Lincoln called for volunteers, and they now weighed their options differently. Even if they were wary of the choice, and concerned about the outcome, they nevertheless chose to support it. Tennessee provides the best illustration of the shift due to having the actual votes to show it, but this was true throughout the South, where the so-called "Plain Folk" might not have wanted secession in Dec. 1860, but by the summer of 1861, with it a fait accompli, large numbers of them were going to put their support behind the war effort nevertheless, and there was, as Williams terms it, "a general enthusiasm" for it.

So again, while Kendi is right, it is important to stress that this doesn't mean there was wide-spread majority opposition throughout. But of course, it also is important to stress that not everyone was in lockstep once the drums of war started to beat. I've written previously here about motivation for the typical, non-slaveowning soldier, and the takeaways I would emphasis there are how the majority bought into the racial order of the South, and did see something they were fighting for. But also how even when we look at the pockets of opposition and resistance in the South, especially Appalachia, they agreed as well, but it was a more abstract concept which helped fuel a strong resistance to participation on the war. This segues into the final bit which builds of that as well, another old answer of mine which I actually rely on Williams for a decent bit, looking at desertion and draft resistance within the Confederacy and I think helps to illustrate the divisions within the South that Williams speaks to and Kendi is mentioning here.

Secession was an extreme option and didn't appeal to the majority at first, but opinion isn't a static thing. The Spring and Summer of '61 saw a groundswell of support once there seemed no alternative to war.... but not everyone felt it, and for those who did, we can find plenty who soured on it soon enough.

Hopefully this annotation of linked answers can help you out a bit, but it isn't exhaustive, certainly, so if there are any follow-ups you might have please ask away.