Writing for New Republic, political scientist Scott Lemieux suggests that Democrats start playing constitutional hardball if the Republicans don't let us govern:
If the Democrats take over Congress and the White House in 2021 with Anthony Kennedy as the median justice—giving them a realistic chance of replacing him—it would be wise for Democrats to hold their fire, barring the Supreme Court serially striking down major legislation on specious constitutional grounds (which the decisions of the Obama era suggest is unlikely).
But what if Donald Trump is able to replace Kennedy, and, God forbid, justices Stephen Breyer and/or Ginsburg as well? There is no good outcome in this scenario. Republicans would have a hammerlock on a nine-member Court for decades. If Trump gets two nominees, this Court is likely to be well to the right of the current Roberts Court and likely to go to war with a Democratic Congress.
Even worse, the decisive nominations would be a product of a Republican Senate refusing to allow a president who won two majorities to fill a vacancy, and then confirming multiple nominees of a president who lost the popular vote by a substantial margin. Court-packing is bad, but allowing an entrenched majority on the Supreme Court to represent a minority party that refuses to let Democratic governments govern would not be acceptable or democratically legitimate, either.
For this reason, it would be very unwise for Democrats to rule anything out. They should be careful not to blow up the power of judicial review without good cause. But if desperate Republicans try to establish an anti-Democratic rearguard on the Supreme Court before they get swept out of office, Democrats have to leave all options on the table.
This reflects what we ancient D&D players know as the "Lawful Stupid" problem. Characters with lawful-good alignment run the risk of trying to do the right thing so much that they fail to do the necessary thing. Think: the Enterprise crew deciding not to save a planet because doing so would violate the prime directive. Or the Democratic Party continuing to assume the Republican Party will follow established political norms even when doing so would cause a temporary shift in power in the United States.