Bob Bauer, who served as White House Counsel to President Obama, writes in Can the Senate Decline to Try an Impeachment Case? Lawfare, Jan. 21, 2019:
The Constitution does not by its express terms direct the Senate to try an impeachment. In fact, it confers on the Senate “the sole power to try,” which is a conferral of exclusive constitutional authority and not a procedural command. The Constitution couches the power to impeach in the same terms: it is the House’s “sole power.” The House may choose to impeach or not, and one can imagine an argument that the Senate is just as free, in the exercise of its own “sole power,” to decline try any impeachment that the House elects to vote.
The Senate has options for scuttling the impeachment process beyond a simple refusal to heed the House vote. The Constitution does not specify what constitutes a “trial,” and in a 1993 case involving a judicial impeachment, the Supreme Court affirmed that the Senate’s “sole power” to “try” means that it is not subject to any limitations on how it could conduct a proceeding.