Based upon the clear understanding of the words in our Constitution and the precedence that has followed since the beginning of our Constitution, the role that the Senate plays in the appointment process is to give "advice and consent" after the President has made a nomination. Nowhere in the practiced history of our Constitution does it give the Senate any legal role in actually appointing a nominee. http://law.marquette.edu/facultyblog/2016/02/23/the-senate-must-consider-supreme-court-nominations-in-due-course/.
Therefore, after the President makes his nominee known to the Senate, the Senate then has it's duty to perform the "advice and consent" protocol long established under law. For the Senate to abrogate it's duty to perform it's function is a clear violation of it's duty and in no way can be considered Constitutional. So what is the Constitutional remedy for the Senate acting unconstitutional? I presume we shall shortly find out.