In declaring that he won’t be voting to allow witness testimony in Donald Trump’s impeachment trial, Senator Lamar Alexander of Tennessee made some interesting observations. First, he acknowledged that the House Democrats had proven that Trump “ask[ed] a foreign leader to investigate his political opponent and…with[held] United States aid to encourage that investigation.” Second, he said that this crime did not rise to a level requiring removal from office. Third, he said that Trump’s blanket noncooperation with the investigation wasn’t even close to being an impeachable offense. While it’s still possible that the Senate will deadlock at 50-50 on the witness question, forcing Chief Justice John Roberts to decide whether or not to break the tie, Alexander’s position probably spells the end of this sad saga in the Senate.

If so, the House Democrats will have some difficult choices to make. They could essentially move on and get back to the ordinary business of working on the budget and passing bills that Trump won’t sign. Or, they could decide to hold a trial of their own, with the potential to impeach Trump a second time before the November election.

If they make the latter decision, they will risk looking obsessed. But, given the stakes, they might feel they have no other choice. They will almost certainly want to hear from John Bolton, who is likely to cooperate this time around. They may also want to hear from Lev Parnas, assuming they can do so without screwing up his prosecution by the Department of Justice. They will also want to vindicate, if possible, their right to get witnesses and documents from the administration, so they’ll have to pursue a legal angle as well. Above all, they’ll want to make sure the full story is told so that people can fairly judge what the Senate did in refusing to look further into the matter themselves before acquitting the president.

For this purpose, they could set up a special committee to basically compile a full investigation unencumbered by time constraints. You could think of it as their own special investigator or prosecutor. Their mission would be to document everything for history in a final report, and the report could make recommendations for people who should be charged or even for new impeachment articles to be passed.

This report might not be complete before the November election, especially given the legal delays in getting resolution on witnesses and documents, but Trump could be impeached even in a second term and even if he is defeated. If he’s guilty, he should not be able to run for or hold high office again.

As time goes by, more information will come out through Freedom of Information Requests and people deciding to talk about what they know, as well as through victories in court. Trump’s acquittal will likely look worse and worse with each passing month and year, and the Senate’s behavior will suffer a similar fate.

This will benefit the Democrats politically, but more importantly, the House Democrats cannot allow this result to stand since it eviscerates Congress’s power to hold a president accountable. As an institution, they need to fight back. Unfortunately, this is something they should be obsessed about and they should be willing to take whatever hit comes along with that.