Politico reports that Senator Merkley (D-OR) intends to file for a court injunction to prevent a quick vote on the Kavanaugh nomination. He claims that would adversely affect his constitutional duty to advise and consent to the nomination.
First, the courts should have no business considering the matter:
Each House may determine the Rules of its Proceedings[.]
—U.S. Const., Art. 1, § 5, cl. 2
If the Senate’s Rules allow for a quick vote, or if the Senate changes or suspends its Rules to allow a quick vote, it’s no one else’s business—except for the voters on election day.
Further, the constitutional duty to advise and consent to nominations does not lie with individual senators but with the body as a whole. So not only is the question not justiciable, Merkley probably lacks standing to sue.