When President Obama selected Garland to fill the Supreme Court seat, Republicans refused to hold a hearing, much less vote. Now that Gorsuch has been selected by Republicans, why can't Democrats refuse to hold a hearing instead of merely filibustering (like Republicans did with Garland)? I know the fact that the Senate is controlled by Republicans is probably part of the answer, but I can't be sure because I can't find an answer either way.
The Senate Judiciary Committee is in charge of holding hearings prior to the confirmation of Supreme Court nominees.
Since Republicans control the Senate, the 20-member committee would consist of 11 Republicans and 9 Democrats. This means that the Republicans hold a majority in this committee, thus they would have enough votes to grant or withhold consent on nominees by the President.
In Garland's case, the 11 Republican members of the committee signed a letter to the Senate majority leader Mitch McConnell on Feb 23, 2016 that they would not hold any hearings for any nominee made by President Obama until the next President takes office.
However, since the Democrats failed to get a majority in the Senate after the 2016 Senate election, the Republicans have a majority in the Senate now and thereby also have a majority in the Senate Judiciary Committee. Thus, they can decide to hold hearings which they did on Apr 3, 2017 with a 11-9 party-line vote.