Democrats are planning on filibustering Neil Gorsuch's nomination to the Supreme Court, but there are some Democrats from states won by Trump who fear this move will result in Senate Republicans getting rid of the filibuster entirely. This concern is misplaced, since if Republicans actually do use the nuclear option, it would be a real political gift to these endangered Democrats.
Currently, Senate Democrats' ability to block the GOP agenda is akin to Schrodinger's cat: It both exists and doesn't exist, and we won't know which it is until Democrats actually try to use it.
From a political perspective, trying to maintain this illusion of possible power is worse than being exposed as having no power at all. The base will get very angry at Democratic senators who don't take part in a filibuster, even if these Democratic senators are convinced it won't work. Under this current dynamic, voters will put some of the blame on red state Democrats for everything that does or doesn't happen in the Senate, even if these senators actually don't have any real power.
On the other hand, if the filibuster is eliminated, Senate Democrats are freed from blame or responsibility. They can clearly and easily say everything is the Republicans' fault. They can honestly tell their base they did everything they could. This is the reason you don't see any liberal base pressure being put on House Democrats, because it is known they can't do anything.
Because of the way Merrick Garland was treated, Senate Democrats have the best moral and political case for a filibuster they will ever have. If they do filibuster Gorsuch and it works, they score a big win. If Republicans eliminate the filibuster, they at least free themselves from blame. Not filibustering, though, is the worst of all possible outcomes. It achieves nothing and makes them responsible.