I don't see this one going anywhere...while it may be comical to watch everyone on both sides get their undies in a bunch about it, the outcome is more than predictable as neither party has shown any sincere effort to take the institution/process seriously.
Basically, the house democrats are doing it due to a hatred of Trump, and are going on a fishing expedition to come up with something of substance to make a case for it...and on the senate side, you have a republican majority who have shown that, even if their were something of substance to be uncovered, they have no intention of taking it seriously or listening to anything they don't want to hear as made clear by the way they voted right down party lines with regards to establishing the rules for the process.
Look at the proposed amendments:
The first, which would allow the Senate to subpoena White House records, was
defeated along party lines, 53-47. A second, to subpoena
State Department documents related to the charges against the president, was also defeated along party lines, 53-47. Schumer immediately proposed a third amendment, to subpoena documents from the White House Office of Management and Budget, which also failed.
Schumer proposed a fourth amendment, to
subpoena acting White House chief of staff Mick Mulvaney, a key figure in events like the unusual freeze on millions of dollars in military aid to Ukraine, which prompted House Democrats to launch an impeachment inquiry. Again, the amendment failed, 53-47.
Schumer agreed to postpone the rest of his amendments until Wednesday, but after a brief negotiation, he introduced a fifth amendment, to subpoena certain Defense Department documents and records. It, too, was defeated, 53-47.
Schumer introduced his sixth amendment, sending the first day of the impeachment trial late into the night. He moved to subpoena the testimony of Robert Blair, a senior adviser to Mulvaney, and Michael Duffey, the associate director of national security at the Office of Management and Budget, who oversees the process for approving and releasing U.S. assistance to foreign countries. And like the five before it, the amendment was tabled on a vote of 53-47.
So to recap, Democratic position: "Let's dig into everything we can to find something of substance we can use against him"
Republican position: "We don't even want the remote chance of something to be uncovered that may make Trump look bad or expose anything, so we're going to block any and all subpoenas
for evidence and witnesses"
Democrats want to fish for evidence, Republicans don't want any remote chance of evidence being uncovered so that 2 months from now, they can say "The Dems had no evidence"
The whole thing is an embarrassment and a joke.