The least dangerous branch begins its 2021 term at a most perilous time — perilous not just for the country but for the Supreme Court itself.

The threat is to the court’s legitimacy, the source of its authority. The existence of the threat has manifested itself in the remarkable fact that three sitting justices — Stephen G. Breyer, Amy Coney Barrett and Clarence Thomas — have recently felt the need to assert that the justices are not, in Barrett’s tart words, “a bunch of partisan hacks.” Chiming in, Justice Samuel A. Alito Jr. on Thursday warned against “unprecedented efforts to intimidate the court or damage it as an independent institution.”

It is evident in the court’s plummeting approval rating. In July 2020, after a term that included overturning a Texas abortion law, protecting “dreamers” and finding that federal civil rights law covers gay and transgender workers, the court’s approval stood at 58 percent in a Gallup poll, the highest in more than a decade.

By July 2021, after a term with more ideologically mixed results, the court’s approval had fallen to 49 percent. In the most recent poll, released Sept. 23, it was down to 40 percent — the lowest since Gallup started testing the question in 2000. A new high — 37 percent — said the court was too conservative, up five points from just a year ago.

Chief Justice John G. Roberts Jr., avowed institutionalist, cannot be sleeping soundly.

Why should public opinion matter, if we want the court, as we should, to be independent and not shift with the political winds? Of course, the justices shouldn’t simply follow the election returns. They have life tenure (for better or worse; term limits would be preferable) precisely to insulate them from political pressure.

But a court whose ideological balance is out of line with that of the country can find itself in dangerous territory, something to keep in mind as the court embarks on a term that already includes major cases that could result in further restrictions on abortion rights and gun regulation and might also sound the death knell for affirmative action in higher education.

We are a closely divided country, but we have a court that is not at all closely divided — not on the cases that matter most.

Consider, since 1969, the last time Democratic appointees constituted a majority on the Supreme Court, Republican presidents have named 15 of 19 justices. During that same period, Democrats have won six of 13 presidential elections, and a majority or plurality of the popular vote in two more. The GOP advantage on the bench is partly a matter of luck about when the vacancies arose (another reason for term limits) and partly reflects Republican willingness to play hardball to prevent Democrats from filling Justice Antonin Scalia’s seat in 2016 and to muscle through Barrett to replace Ruth Bader Ginsburg before Donald Trump’s defeat in 2020.

So would I be lamenting if there were, instead, a 6-to-3 liberal majority? Fair question, with two quick answers. First, a court tilted too far in either direction is unhealthy. Second, on this court, even the 6-to-3 division understates the tilt: The conservatives are much further to the right than the remaining liberals are to the left. This is the most conservative court since the 1930s, and, uniquely in U.S. history, one whose ideological blocs align precisely with the party of the president who appointed them.

This systemic and entrenched disconnect between public opinion and the judicial philosophy of the court’s majority creates a problem when it comes to assuring that the court’s decisions are accepted and followed. As Breyer points out in his new book, the court has no independent authority to enforce its rulings; that depends on public acceptance. He praises the country’s reaction to Bush v. Gore, the 5-to-4 ruling in which the court — over Breyer’s dissent — effectively awarded the presidency to George W. Bush.

“Despite the huge stakes involved, despite the belief of half the country that the Court was misguided, Americans accepted the majority’s holding without violent protest, without the throwing of stones in the streets,” Breyer observes, citing then-Senate Minority Leader Harry M. Reid (D-Nev.). “And the losing candidate, Al Gore, told his supporters, ‘Don’t trash the Supreme Court.’”

Breyer takes this as a good-news story about our ingrained national “habit” of respecting the court’s authority. I read it and think: We’re not in 2000 anymore. Were you watching on Jan. 6? This is a much more polarized country, and a much more polarized court.

Two quotes from Justice Elena Kagan, several years apart, highlight the current danger.

In 2018, as Brett M. Kavanaugh’s Supreme Court confirmation hearings were exploding in partisan rancor, Kagan observed, “The court’s strength as an institution of American governance depends on people believing it has a certain kind of legitimacy, on people believing it’s not simply just an extension of politics, that its decision-making has a kind of integrity to it. If people don’t believe that, they have no reason to accept what the court does.”

Fast-forward to Kagan’s recent dissent from the court’s decision to let Texas’s flagrantly unconstitutional six-week limit on abortions take effect. She focused on the court’s increasing use of its emergency decision-making power — its “shadow docket” — which, she said, “Every day becomes more unreasoned, inconsistent and impossible to defend.”

Kagan 2018 emphasized the need for the public to believe that the court’s decision-making “has a kind of integrity to it.”

Kagan 2021 seems to despair of the institution’s capacity to meet that test.

Where does that leave the court? Where does that leave the country?