So, what options would the Senate have if the House voted to impeach on two unconstitutional grounds? Would it be required to conduct a trial based on "void" articles of impeachment? Could it simply refuse to consider unconstitutional articles? Could the president's lawyer make a motion to the Chief Justice — who presides over the trial of an impeached president — to dismiss the articles of impeachment on constitutional grounds?
This is uncharted territory with little guidance from the Constitution or history. There are imperfect analogies that may be informative. If this were an ordinary criminal case, and a grand jury had indicted a defendant for a non-crime (say, having gay sex) or an unconstitutional crime, the trial judge would be obliged to dismiss the indictment and not subject the defendant to an unconstitutional trial. Impeachment, however, is not an ordinary criminal proceeding. So, the analogy is not directly on point. But impeachment by the House is similar in many ways to indictment by a grand jury, and a removal trial by the Senate is similar to a criminal trial, including being presided over by a judge. It is entirely possible that the president's lawyers may file a motion seeking dismissal of the impeachment as unconstitutional. It is impossible to predict whether such a motion would be entertained and if so, how it would be decided.
Another option would be for the president's lawyer to seek judicial review of the House's unconstitutional action. Despite the fact that the Constitution says that the House shall be the "sole" judge of impeachment, two former justices have opined that there might be a judicial role in extreme cases.
The most likely option for the president — and the one hinted at by White House sources — is for the Senate to conduct a scaled down trial focusing on the constitutional defects in the articles of impeachment. No fact witnesses would be called: that would turn the proceeding into a he said/she said conflict with no clear resolution. Only legal arguments — neater and quicker — would be presented before a vote was taken.
UPDATE: All Professor Dershowitz's hypotheticals fail to address all contingencies. For example, what happens to Zelensky's daughter?
How completely unhinged Democrats have become in this Impeachment hearing?— Benny (@bennyjohnson) December 12, 2019
Member of the Judiciary Committee Hank Johnson (D-GA) just said Impeachment is justified because:
1. Trump taller than Prez. Zelensky
2. Trump had Zelensky's daughter "in the basement duck taped"