"Court packing" is a term that began to circulate in the modern context following the shoddy treatment of Merrick Garland, President Obama's 2016 nominee to the Supreme Court. It is rightly viewed as a dramatic tactic, but if Brett Kavanaugh is confirmed, a future government controlled by Democrats is likely to pursue that option as the best way to rebuff a conservative Court majority viewed as illegitimate.
I have watched Republican politicians snatch defeat from the jaws of victory many times: Invading Iraq and squandering the political capital gifted to them by 9/11, refusing to take "yes" for an answer on entitlement cuts when a Democratic President (Obama) put them on the table in 2011, and of course, nominating a polarizing, buffoonish candidate for President in 2016 who, despite his victory, looks to be the one who will bear the blame for a huge anti-GOP wave in 2018.
Today, Republicans, specifically in the U.S. Senate, stand on the precipice of another blunder which will give future Democratic Presidents and Democratic congressional majorities the ammunition they need to dilute what should be a generation-long conservative majority on the highest court in the land. Current Supreme Court nominee Brett Kavanaugh is facing a mountain of sexual harassment and assault allegations. Lesser charges have brought down members of Congress, such as Minnesota Senator Al Franken, but Senate Republicans and the White House are pressing ahead, refusing to call for an FBI investigation of the allegations. We are facing a situation where a man, credibly accused of sexual assault, could end up on the Supreme Court, and become the fifth vote to strike down a woman's right to an abortion.
Political scientist David Faris has made the Liberal case for "court packing" on the basis of a systematic breakdown in norms around the Supreme Court nomination process. The basic notion is that these norms have prevented massive ideological swings on the Court over the last few decades. The norms, Faris says, have now been shredded, providing an opportunity to thrust hard line Justices onto the Court come hell or high water. He rightly points to the nomination of Merrick Garland in 2016, which Republicans ignored for the better part of a year. This enabled the party to gin up support for Donald Trump from their base and ultimately allowed them to preserve a conservative vote on the Court. To confirm Justice Neil Gorsuch, the Republican majority voted to change long-standing Senate rules requiring a 60-vote threshold for Supreme Court nominees. That's two massive breaks from the way the process has been handled in the past.
With Brett Kavanaugh, you have a situation where an FBI investigation would be a normal part of the process, no matter when the allegations were unearthed. Anita Hill's accusations against Clarence Thomas, for instance, were investigated prior to her appearance before the Senate Judiciary Committee. If Judge Kavanaugh is confirmed without any effort by Republicans to clear his name through an impartial investigation, he will be viewed as a tainted nominee, one who certainly should not play any role in deciding cases related to women's rights.
The Supreme Court currently includes one Justice occupying a seat that, under normal circumstances, would have been filled by a Democratic President. If the current vacancy were filled by a conservative without the sexual violence baggage that surrounds Brett Kavanaugh, you would likely still see 5-4 rulings overturning a woman's right to an abortion, permitting corporations to use constitutional rights as pretext for abusing real people, striking down legislative efforts to protect the vote, clean air, clean water, and the right of workers to organize. The parade of horribles, from a progressive standpoint, would be long and infuriating. Those same 5-4 decisions with Kavanaugh on the bench are likely to provoke the kind of backlash and energy on the left that will convince Democrats in Congress and the White House to take drastic action not seen since the presidency of FDR. There is no constitutional language prescribing a specific number of Supreme Court Justices. All it takes to make a change, is a President and a Congress, fed up with seeing initiatives blocked by an ultra-conservative, corporatist Supreme Court.