I’m not so sure. The Senate would find the pressure quite high by stalling a SCOTUS seat for six months or more. He’d have to play his cards right for sure.
The 800 pound gorilla in the room is that the Democrats are on the defensive in SCOTUS because their solid four justices are all older than Clarence Thomas, Alito, and Roberts, and most of them are older than Scalia. It would be a surprise if the next opening were not caused by retirement (or otherwise) of a member of the liberal wing of the court. And right now for practical purposes Justice Kennedy is SCOTUS. One more nomination like Thomas or Alito or Roberts, and the Democrats will have to convince not only Justice Kennedy but another, more conservative, justice in order to prevail.I don't consider that a mere matter of a little pressure from Republicans will convince the Senate Democrats to allow that to happen if they have any choice at all. And indeed the Republicans in the Senate, with people like Arlen Spector and John McCain in their number, are squishy enough that I can't imagine them fighting that battle successfully. It would be hard enough in the next term, even with a conservative POTUS and with a Republican pickup of a seat in the Senate, which seems unlikely, to get a good justice seated. Of course, if it got to where two of the liberal justices resigned, SCOTUS would become unambiguously conservative even if the Democrats prevented the vacancies from being filled indefinitely.