What legislative action could Congress possibly pursue against the Supreme Court?

Question

In the recent Supreme Court case New York State Rifle and Pistol Association INC v. City of New York, an amicus curiae was filed by 5 Democrat US Senators basically threatening to pursue legislative action against the court if they didn't dismiss the case. (On pages 2-3 of Justice Alito's dessent at the above link.)

A prominent brief supporting the City went further. Five United States Senators, four of whom are members of the bar of this Court, filed a brief insisting that the case be dismissed. If the Court did not do so, they intimated, the public would realize that the Court is “motivated mainly by politics, rather than by adherence to the law,” and the Court would face the possibility of legislative reprisal. Brief for Sen. Sheldon Whitehouse et al. as Amici Curiae 2–3, 18 (internal quotation marks omitted).

What legislative action could they possibly pursue? Even assuming there is some theoretical thing they can do, what hope would they have to actually get it passed considering the strong Republican majority in the Senate?

Answer 1

First point... Having read this Amicus Brief all the way through, I can tell you that nowhere does it talk about 'legislative reprisal'. Nothing close to that terminology exists; it is nearly complete fabrication. There's only one phrase that comes close, namely that the public might demand that the court be “restructured in order to reduce the influence of politics.” And in fact, if it becomes a public belief that the court is unduly influenced by political interests, then it would be their natural right to call for restructuring, just as the public has called for restructuring of the other branches, through things like term limits, campaign finance laws, the Freedom of Information Act, electoral reforms, ending gerrymandering, and etc.

Second, the legislative branch in the US has the sole power to enact legislation. In fact, Article III of the constitution states:

The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. (thanks to Bobson, for pointing that out in comments)

Congress is the most powerful branch of government (when they choose to act that way, which is rare these days), and should they decide to restructure the judiciary, they can. If the public demands it, well... Far from being a reprisal, it would be Congress' sworn duty to carry out such restructuring. Congress is meant to represent the interests of the electorate, and if the interests of the electorate mean cleaning up the courts, that is within Congress' purview. They merely need to sit down and write new legislation.

Third, most people forget that the Congress has the power to impeach and put on trial not just the president and vice president, but also "all civil officers of the United States", a category which includes members of the judiciary (excluding military justices). Since black-letter impeachment covers bribery and misdemeanors — with influence peddling falling squarely within those domains in federal law — Congress has a fairly big stick it can wield should it decide to pursue this kind of restructuring.

Last... Yes, the GOP currently holds a majority in the Senate. However, unless we abandon representative democracy and switch to an authoritarian form of government, the GOP will not always hold the Senate. Though it may not seem like it from the Trump-era 24 hour news cycle craziness, most Congresspeople and members of the Judiciary are keenly aware that political fortunes change, and all have long memories. They generally act with due deliberation to prevent the arc of history from crushing them underfoot. No one on any court wants to be the author of the next Dred Scott decision — the decision the precipitated the Civil War, was obviated by Congressional amendment, and marked in history as a shameful misjudgment — and a reminder that such an outcome is possible is both well-given and well-taken.

The balance of power between the branches of the US government is not a passive thing. If one branch starts to misuse or over-reach its power, the other branches can and ought to actively intervene. That is how the system is designed. Misrepresenting such actions as 'reprisals' is biased and ignorant; you should find better news sources if that is the kind of information you are receiving.

Answer 2

Whether Alito is merely posturing there given the current (party) split of Congress or whether he had a longer time-frame perspective in mind is hard to say (just from that passage).

But historically speaking, there was a well-know threat of FDR to "pack the court" with more justices (favorable to the president). That threat took the form of a bill, the Judicial Procedures Reform Bill of 1937. So if the executive and Congress happen to align on such an issue, they can in theory reform/change the Supreme Court in quite substantial manner.

In 1937 however, the Senate also proved quite a spanner in the adoption of that bill:

Roosevelt's legislative initiative ultimately failed. The bill was held up in the Senate Judiciary Committee by Democratic committee chair Henry F. Ashurst who delayed hearings in the Judiciary Committee saying, "No haste, no hurry, no waste, no worry—that is the motto of this committee." As a result of his delaying efforts, the bill was held in committee for 165 days, and opponents of the bill credited Ashurst as instrumental in its defeat. [...]

As future Chief Justice William Rehnquist observed:

President Roosevelt lost the Court-packing battle, but he won the war for control of the Supreme Court ... not by any novel legislation, but by serving in office for more than twelve years, and appointing eight of the nine Justices of the Court. In this way the Constitution provides for ultimate responsibility of the Court to the political branches of government. [Yet] it was the United States Senate - a political body if there ever was one - who stepped in and saved the independence of the judiciary ... in Franklin Roosevelt's Court-packing plan in 1937.

Interestingly enough, more recently Alito has shown some willingness to overturn some cases from that New Deal era. So maybe he had that kind of long[er] view in mind, who knows...