So here’s the thing, a sitting President of the United States has the constitutional authority to nominate someone to the Court right up until the moment the next guy takes the oath of office. Last-year-of–term appointments are almost always challenging and no president ever expects a smooth confirmation process, especially for a nomination to the Supreme Court. Anyone who tells you something different is lying.
Now over in the Senate they have the constitutional responsibility for providing advice and consent to the presidential appointment. What “advise and consent” means is determined entirely by the Senate. That means they’re well within the scope of their authority to call a vote immediately or delay a vote for the next 57 years. Anyone who tells you something different is lying.
You may have noticed I didn’t raise any topic of the politics of court appointments, just a bit of commentary on the mechanics. I’ll leave it to others to try telling you about the politics involved. Just try to remember that if your news source is telling you the president has to do something or the Senate has to do something else they’re probably lying to you. The scope of what the executive and legislative have to do in this situation is pretty well defined if anyone would bother consulting their pocket Constitution before running off at the mouth.