What does it mean to pack the courts, is it the appropriate response and would it make the courts less of a partisan battleground issue?
People often use "court packing" to describe changes to the size of the Supreme Court, but it's better understood as any effort to manipulate the Court's membership for partisan ends. A political party that's engaged in court packing will usually violate norms that govern who is appointed (e.g., only appoint jurists who respect precedent) and how the appointment process works (e.g., no appointments during a presidential election).
Seen from this perspective, the Barrett appointment is classic court packing. The president nominated a hardline conservative who appears to question major parts of U.S. constitutional law. And the Senate majority changed its procedural rules – invented to deny Merrick Garland a hearing – to ram through the nomination as people were voting.
If Democrats respond to the Barrett appointment by expanding the size of the Court, the immediate effect will be to further diminish the Court's standing and make it hard for anyone to take the Supreme Court seriously.
Paradoxically, I think that's a good development. Restoring a sense of balance to the Court will require Republicans and Democrats to come together and agree on new rules for how justices are chosen and the kind of jurists who serve on the Court. As long as Republicans play hardball with the appointments process and Democrats fail to respond in kind, Republicans have no reason to come to the table. Why bargain when you are getting everything you want?