Not even FDR managed to pack the court, though he tried -- and arguably the threat of doing so caused the court to stop striking down his programs, so FDR got what he wanted. Democrats seek to recreate the same dynamic by threatening to pack the court with four (!!) more justices despite holding only very narrow majorities in the House and technically no majority at all in the Senate (Kamala Harris' tie breaking vote in the only thing giving them primacy there).
Whether by packing the court directly or by threat of doing so, the Democrats plan to neutralize the potentially significant 6-3 advantage Republicans now hold on the court.
Unfortunately, Roberts has already all but switched sides, making the practical majority 5-4. And even that majority was insufficient to decide the electoral fraud cases in 2020. If the Democrats do succeed in packing the court, they will hold an 8-5 majority. And their justices vote in lockstep when required.
Passage of this legislation would be a disaster with generational consequences.