The Senate Democrats have a huge dilemma. They spent years complaining about Republican obstructionism in general and the last several months complaining that the Senate Republicans needed to "do their Constitutional job" and approve President Obama's nominee for the Supreme Court. But now that President Trump has nominated someone, the Democrats suddenly turned obstructionist.
There is no good reason for opposing Judge Gorsuch. He is eminently qualified and he will not tilt the court further to the right. There are some ruffled feathers on the left because Obama's nominee didn't get a hearing but the precedent of the opposing party stopping lame duck appointments goes back to 1992 and both Barack Obama and Joe Biden supported it as senators.
The main reason there is any controversy is that the left hates President Trump with a white hot passion. They don't want to see the Democrats in Congress cooperating with Trump on anything.
The problem for the Democrats is that it makes what the Republicans did against Obama look mild by example. The Democrats are raising the level of obstruction. This will haunt them in two ways. When they inevitably return to power, the Republicans will use every trick that the Democrats have used. In the meantime, the Republicans have every excuse to throw away the rule book and use the "nuclear option" - changing the rules by a simple majority vote. The Democrats already did this for everything except Supreme Court nominees, something they are surely regretting right now. Doing away with the filibuster for Supreme Court nominees will make it easier to confirm more polarized justices. That's one of those things that's only good when your side can do it.
So the Senate Democrats have strong reasons to allow Judge Gorsuch to be confirmed. But that will anger the base and will probably lead to some primary challenges.
For many Senators, there is no good choice. Doing the right thing will hurt them and doing the wrong thing will hurt the country. So they have a dilemma.