Honestly, there isn't much that Senate Democrats can do to fully prevent a Republican majority, slim though it may be, from seating another Supreme Court nominee from Donald Trump, illegitimate as that nomination might be. What they can do, however, is delay it until after the election. And after the election, the chances of blocking it are probably better. There could very well be some defeated Republicans who won't have anything to lose anymore and might just decide not to seal their legacies with something so ignoble as this. Additionally, if they can delay throughout November, Democrats will likely have a new member—Arizona's Mark Kelly, who could be seated as early as Nov. 30 by Arizona law.
To that end, congressional procedural experts have drawn up a memo that's reportedly circulating on Capitol Hill that details the myriad options available to Democrats—both in the House and Senate—to eat up Senate time and prevent Senate Majority Leader Mitch McConnell and Judiciary Committee Chairman Lindsey Graham from rushing the nomination through before Nov. 3. There's no silver bullet here for Democrats to stop the confirmation, but there are tons of BBs.
We talked about a lot of what the Senate can do in this post, but didn't explore the House's options. Like sending over articles of impeachment. (I nominate Attorney General Barr for that one, personally.) The House could act on Senate bills pending in the House, amend them, and send them back as privileged—the Senate could be forced to act on them.
In a perfect world, Sen. Chuck Schumer and team would deploy all of them. As of now, they are not. As of now, with no official appointment, they don't have to. McConnell is going to have to deal with the continuing resolution the House just passed to fund government through Dec. 11 early next week, because the deadline is midnight Wednesday.
Republicans are not devoid of ways of trying to keep Democrats from doing this—they can keep putting up things for unanimous consent, like this resolution expressing support for the Pledge of Allegiance. Now, what Democrats could do is use every tactic from Republicans to engage the Republicans in hours of debate on them. That's something they need to be doing anyway: standing on the floor punching holes in Republican arguments and making them answer for their blind loyalty to Trump.
Democrats can start doing these things now to show McConnell their resolve to stand together in making his life hell, dissuading him from trying to push through the nomination before the election. They can use a wide variety of procedural tactics to force Republicans who need to be spending all their time on their reelection at home to stay in Washington, D.C., having to be subject to a call to come to the chamber at any given time. Sowing as much unrest as possible among those Republicans is always helpful.
It's about meeting McConnell's fire with fire; it's about not being steamrolled, and not letting him and Trump further foul the Supreme Court of the United States.