With Anthony Kennedy's retirement, the Democratic minority in the Senate does not have great options. Matt Glassman at "Notice and Comment, " a blog from the Yale Journal on Regulation and the ABA Section of Administrative Law & Regulatory Practice
How could the Democrats increase the costs of considering the nomination? By using obstructive tactics to slow down other issues the Senate majority would like to take up. Instead of agreeing to yield back post-cloture time on other judicial nominations, they could demand (and use) the full post-cloture debate period. They could filibuster all general legislation. They could demand recorded votes for things routinely done by voice vote or unanimous consent. They could refuse to vote for cloture on appropriations bills (which require 60 votes), and shut down the government. In essence, they could conduct a cross-issue filibuster, in the hopes that a number of Republican Senators would decide that the costs of pursuing the nomination were too high in terms of other legislation they would like to pass.
This is highly unlikely to work. First, a SCOTUS seat is something the Republicans are willing to pay a very high price for. Even if you could stop all legislation and every other judicial nominations dead in its tracks (you can’t), it might not persuade them to abandon a SCOTUS confirmation. Second, if the Democrats resorted to an all-out general dilatory posture that raised the costs to an unacceptable level for some GOP Senators, the Republicans might use the nuclear option to change the rules in order to restrict the dilatory tactics. Finally—and most importantly—aggressive hardball tactics are constrained by public opinion. Even if Democrats pursued a dilatory strategy that somehow successfully blocked the nomination through the election, it would be a pyrrhic (and short) victory indeed if the cost was a net loss of 4 Senate seats, or control of the House. The fear of that public backlash creates a practical prior restraint on even attempting many theoretically-possible hardball tactics.