If the American people want a liberal, activist Supreme Court legislating from on high as the supreme branch of power, they'll decide that in November.
And if they want a reserved, more conservative court, one that doesn't dictate to the legislature or goes out of its way to supersede legislative (meaning the people's) prerogative, Americans will decide that too.
All the rest is meat puppet mud wrestling. Yes, President Barack Obama has the right to appoint a successor. And yes, the Senate, now under Republican control, has the right to dismiss it.
It's a meaningless question to ask "what do the people want" as if "we" has a definable meaning. I want something, you want something, and others want something entirely different. However, in fight, there has to be some rationale ...