One way the Republicans can still obstruct nominations is to focus on hearings in committee. They can refuse to grant unanimous consent for committees to hold hearings in the first place, or they can refuse to show up for committee hearings, thereby denying a quorum for those committees. I don’t know how far they will be willing to go with these tactics, but I assume they will at least be willing to use them in a handful of targeted cases.
I think that the Senate Democrats have the ability to change the rules on hearings and quorums, but I don’t have a clear idea about how willing they will be to exercise those options. My guess is that they will tolerate a modest degree of obstruction but will strike back with fury if the Republicans try to make such obstruction a routine replacement for their filibustering tactics.