First off: horrible, horrible news. I was sick to my stomach last night when I heard the news. RBG was a great justice, and wrote some tremendous opinions. This country will miss her tremendously.
Second: In principle, I would agree that Trump should nominate a replacement, and the Senate should go through the process of holding hearings and voting to confirm/deny. This is what the Constitution specifies. However, the Republicans have no principles and do not care what the Constitution says. This has been shown repeatedly, and, specifically as to this topic, was on full display in 2016 after Garland was nominated. Of course, we all knew then that the Republicans were full of ****. That being said, should we stand on our principles (i.e. regardless of what happened previously, the Constitutionally correct position would be to go through the nomination/confirmation process) or push the Republican argument re Garland (i.e. no appointments/confirmations during election season)?
Third: To the extent that Trump nominates a replacement (almost 100% certainty), and the Senate takes up the confirmation process (also an almost 100% certainty), I think it makes sense to fight like hell to delay the confirmation process until Election Day (or once the results from Election Day are known, which may take a few weeks/months). Perhaps there are also enough Republican Senators to assist with ensuring that the confirmation process does not end until after the results from the election are known. Then, there are four scenarios: (a) Biden wins, and the Democrats take over the Senate (and keep the House); (b) Biden wins, but the Republicans keep the Senate; (c) Trump wins and the Republicans keep the Senate; and (d) Trump wins and the Democrats take over the Senate.
My initial thoughts on how to play this out under these scenarios:
Under scenario (a): Play the principled stance (i.e. take up the nomination and confirm if appropriate during the lame duck session). Then, in the afternoon of January 20, 2021, kill the filibuster and pass legislation increasing the size of the Supreme Court to 15 justices, and have Biden nominate 6 additional justices. (Also, give statehood to DC/PR/others, presuming they want it. I would just caution that PR may not be the solid blue state that a lot of people think it is, although I do believe it would lean that way.) Democrats get the best of both worlds: high ground as to taking a principled and Constitutionally correct stance, and a Supreme Court that reflects the actual populace.
Under scenario (b): Attempt to delay until after January 20, 2021. This will likely be unsuccessful, but hopefully playing Republican hypocrisy over the airwaves for 2 years (to the 60% of the country that would listen and hopefully be motivated to vote) until the 2022 midterms might help reclaim the Senate, particularly in what looks like a good map favoring Democrats. Presuming the Democrats take over the Senate in 2022, see legislation discussed above under scenario (a).
Under scenario (c): This is, obviously, the most concerning scenario. Realistically, the democracy as we know it would end, and I can only imagine how deeply Trump would destroy the country and tilt the playing field to the right. However, and assuming there is at least the potential to save the country, I believe playing the principled stance would probably make the most sense. It won't matter delaying, and at least Democrats would have a principled argument to make over the following 2 years with a look at taking over the Senate in 2022. Then hopefully Democrats would regain the trifecta in 2024 and could follow the legislative path discussed above under scenario (a).
Under scenario (d): This is highly unlikely to play out this way, but I think the principled stance makes the most sense. Going 4 years without a Ninth Justice would be a politically difficult posture to take. Similar to scenario (c), the goal here would be to retake the the trifecta in 2024. Then follow the legislative path discussed above under scenario (a).
Fourth: I think a cutesy play for the Republicans would be to nominate Garland. They could "rectify" their error from 2016, while reaping the benefits of keeping the Court conservative from 2016-2020, and then replacing RBG with a moderate Garland. Democrats would also be put in a bit of a bind on pushing for any delay. Of course, Trump would never nominate him, and if he did his base would go ballistic (perhaps both literally and figuratively), but it would provide the Republicans in the Senate some cover for the 2016 travesty.