In addition to an abuse-of-power allegation, Democrats leading the impeachment inquiry into Donald Trump are said to be building a case against the president for alleged obstruction of justice.

But it had not occurred to anyone that the obstruction in question might literally amount to the physical obstruction by Republican lawmakers of impeachment proceedings.

The chief justice of the supreme court is supposed to oversee an impeachment trial in the Senate, if it comes to that, but a football referee with a whistle would have been more useful on Wednesday, when a group of 41 Republican members of Congress invaded the secure room where impeachment witnesses are being questioned.

The invaders protested that they had been excluded from the proceedings. No matter that dozens of Republicans are sitting in on the hearings, where closed-door status is not remarkable and entirely appropriate, according to Republicans themselves. No matter that 13 of the 41 Republicans who protested being banned from the proceedings in fact had access to the room and had actually attended the hearings, according to the Washington Post.

In light of those facts, Republicans’ invasion charade might seem desperate, but it points to an important feature of Trump’s overall impeachment defense, analysts warned, and one that opponents of the president might underestimate.

Trump’s playbook when he faced special counsel Robert Mueller was to seek to discredit the investigation as a corrupt, partisan “witch-hunt” with no grounding in fact. He is pursuing a similar strategy now, with the help of young Republican members in Congress who recognize that the fastest route to building power – and fame, and perhaps even wealth – in today’s Washington is to be seen defending the president on TV.

Under this strategy, the substance of the impeachment inquiry does not matter; it only matters what the inquiry looks like to the American voters who stand behind the members of Congress in whose hands Trump’s fate lies. Each degree that Trump is able to move the conversation away from his alleged misdeeds and toward supposed flaws in the process or poison in the politics represents a success for him.

To that end, Trump in the last week has used racially inflammatory language to describe the inquiry, attacked Republicans who oppose him as “human scum”, and repeatedly demanded that the identity of the whistleblower in the Ukraine affair be revealed. He has sprinkled some conspiracy dust on top, claiming on Thursday that the impeachment inquiry is part of an “insurance policy” held by the “deep state” to circumvent or override his election.

And Trump congratulated the “tough, smart and understanding” Republicans who invaded the hearing room, some of whom “asked to be arrested”, according to Chad Pergram of Fox News.

“They wanted the optic of being frog marched out of the SCIF [secure room] in front of TV cameras,” Pergram wrote. “That would help with [the] GOP narrative of Democratic process abuse.”

None succeeded in being arrested, although they stayed long enough to order pizza.

The Republican demands for “transparency” in this early stage of the impeachment inquiry has a certain flavor of myopia about it, analysts noted, speculating that public testimony, for example by Bill Taylor, the top US diplomat to Ukraine, could be even more damaging for Trump than was Taylor’s private testimony on Tuesday, which shocked lawmakers.

“Mark my words,” wrote former FBI special agent and commentator Asha Rangappa, “when it comes time, these same people are going to try their damnedest to keep these witnesses from testifying publicly.”

As Taylor testified, Trump met with lawyers at the White House – notably omitting the embattled Rudy Giuliani – and called congressional Republicans to demand better coordination and a more aggressive impeachment defense, the Wall Street Journal reported. But Republicans complained that they did not have talking points to follow and it was unclear whom, apart from Trump, they should be taking their cues from.

Other planks of Trump’s defensive strategy appear improvised. Steve Bannon, he of Trump’s successful presidential campaign, has announced a daily radio show run from his basement to defend Trump, imagining it as “an outside war room”. On the show, Bannon and his co-hosts have counseled Trump and Republicans to throttle back on the conspiracy theories, respect the political chops of the House speaker, Nancy Pelosi, and treat impeachment as a serious threat.

And the South Carolina senator Lindsey Graham, a stalwart Trump defender, called a news conference on Thursday to announce that he would introduce a resolution in the Senate condemning the impeachment inquiry.

Graham’s rush for the cameras came in seeming response to mounting pressure on him, exerted by the Trump inner circle including Donald Trump Jr, to do more to protect the president, Axios reported.

Graham had some advice for Trump this week, as well, telling reporters that it would be good for the White House to assemble a communications team with legal experience to be specially dedicated to impeachment.

The White House communications director, Stephanie Grisham, responded to that advice with an attack on Democrats.

“It’s hard to message anything that’s going on behind closed doors and in secret,” she was quoted by Bloomberg News as saying, ignoring the fact that 48 Republicans, including the vice-president’s brother, sit behind those “closed doors”.

“It’s like you’re fighting a ghost. You’re fighting against the air. So we’re doing the best we can.”