According to Fox News, Paul plans to challenge Roberts’ authority to censor Senators in their own chamber:

Chief Justice of the United States John Roberts blocked Kentucky Republican Sen. Rand Paul from posing a question during the Senate impeachment trial Wednesday that would have named the alleged whistleblower at the center of the case, Fox News is told — and Paul may try to force the issue during the question-and-answer session that begins Thursday afternoon.

Roberts, for now, has ball control because he actually receives the questions in note cards from senators, then reads the question aloud in the Senate chamber to be answered by either House Democratic managers or Trump’s defense team. But Fox News has learned Roberts may soon lose his grip on the proceedings amid a torrent of criticism both inside and outside the Senate.

The Federalist co-founder Sean Davis condemned what he called Roberts’ “arbitrary and unilateral censorship of senators and Senate business,” and reported that Roberts had initially sought to block even general questions of the intelligence community whistleblower. When Republicans threatened a vote rebuking Roberts on the record, Davis reported, Roberts backed down and decided only to prohibit mentioning the whistleblower’s name. …

Asked by Fox News whether Paul, who has long raised concerns about possible intelligence community overreach, would press the issue during the upcoming question period, a spokesman for the senator told Fox News only, “tbd” — short for “to be determined.” Last year, Paul was vocal about wanting testimony from the whistleblower on the record.

Roberts’ decision seems difficult to justify on its face, if it in fact does not reflect the will of the Senate. Congress has passed laws protecting whistleblowers in part by shielding their identity, but Congress is not usually subject to such laws when they are in session and in debate. Furthermore, it’s tough to identity more weighty circumstances than an impeachment trial in which all information should be available from the record to debate. House managers have insisted that the whistleblower’s identity is not germane to their case, but that stopped being their decision when they transmitted the articles of impeachment to the Senate. As Patrick Philbin laid out last night, there are significant questions left unanswered about the whistleblower that go directly to the president’s defense.

And it’s not the chief justice’s decision ultimately, either. Once again, this reminds us that Roberts has little authority as Presiding Officer. Roberts can make rulings from the chair, but they only have force if none of the senators object to them. In that sense, he’s no different than the members who sit in the chair each day and are tasked with running the Senate’s business with as much efficiency as possible. Any rulings they make are subject to a floor vote if a single member objects to it.

Paul could, according to the rules, object to Roberts’ decision to reject his question. That would force either a floor vote or a retreat by Roberts. But would Paul win such a vote? Not likely, Politico reports:

Roberts signaled to GOP senators on Tuesday that he wouldn’t allow the whistleblower’s name to be mentioned during the question-and-answer session that started the next day, the sources. Roberts was allowed to screen senators’ questions before they were submitted for reading on the Senate floor, the sources noted.

Senate Majority Leader Mitch McConnell (R-Ky.) and other top Republicans are also discouraging disclosure of the whistleblower’s identity as well. Paul has submitted at least one question with the name of a person believed to be the whistleblower, although it was rejected. Sen. Mike Lee (R-Utah) composed and asked a question regarding the whistleblower earlier Wednesday that tiptoed around identifying the source who essentially sparked the House impeachment drive.

“We’ve got members who, as you have already determined I think, have an interest in questions related to the whistleblower,” Senate Majority Whip John Thune (R-S.D.) said. “But I suspect that won’t happen. I don’t think that happens. And I guess I would hope it doesn’t.”

Paul seemed undaunted last night anyway:

“It’s still an ongoing process, it may happen tomorrow,” Paul told reporters.

In order to win, Paul will need 51 votes in support of either freeing the specific question or eliminating Roberts’ ability to censor questions at all. Paul will need to argue that revealing the identity of the whistleblower will be itself important to a decision whether to acquit or convict Trump, which will be tough to argue given that Trump already has an acquittal in the bag. Otherwise, this will look gratuitous, and Senate Republicans have enough headaches out of this process as it is. If McConnell and Thune aren’t enthusiastic about this idea, just imagine what Mitt Romney, Susan Collins, Cory Gardner, and Lisa Murkowski will think of Paul’s challenge.

The other argument Paul could use is that Roberts is overstepping his authority, but that’s not going to win over a lot of votes in the end. Roberts doesn’t really have any authority that the Senate hasn’t granted him, and a vote on this point will likely prove that.