A case in point is his claim, tweeted on March 4, that former President Barack Obama had ordered wiretaps on Trump Tower during last year's election - which some in the media have taken to describing as an "evidence-free" allegation.

Trump was positively jaunty in defending his claims, in a Wednesday TV interview. But in a stinging rebuke to a sitting president, the chairman of the house intelligence committee, Republican Devin Nunes, told reporters he had seen nothing to make him believe there had been such a surveillance operation.

As blunt as he was unambiguous, Nunes said: "We don't have any evidence that that took place."

Seen as a trusted Trump loyalist, particularly after serving on the presidential transition team, Nunes left little to the imagination, adding: "In fact, I don't believe ??? in the last week of time, people we've talked to, I don't think there was an actual tap of Trump Tower."

And in case his point was lost, Nunes made the point that if Trump's claim was to be taken literally, "then clearly the president is wrong."

Even Trump's newly minted top law officer seems perplexed. As attorney general, Jeff Sessions could reasonably be thought to have provided the proof on which Trump based his wild claim, but encountering reporters in Richmond, Virginia, Sessions said that he had not given Trump any reason to believe he had been wiretapped.

GOP congressmen on the various house and senate committees investigating Trump's links with Russia also have had enough, threatening to issue subpoenas against the White House and the FBI and/or to block presidential appointments until they get answers - in particular, that of Rod Rosenstein as deputy attorney general.

FBI director James Comey, whose response to Trump's tweeted claim was a demand that his superiors in the Justice Department issue a denial, which was not forthcoming, is now scheduled to testify before the house intelligence committee on March 20, during the committee's first public hearing on the Russia business.

In confirming Comey's appearance, the committee's senior Democrat Adam Schiff challenged the conflict in claims by White House spokesman Sean Spicer who, on the one hand, said he was not aware of any investigation targeting Trump; but on the other, insisted the president spoke accurately when he said he had been wiretapped by Obama.

"Those two things cannot both be true unless he is suggesting that the FBI was engaged in a rogue operation unsupervised by a court to wiretap Trump Tower," Schiff said. "There is absolutely no evidence of that and no suggestion of any evidence of that."

Republican Senator and chairman of the judiciary committee Chuck Grassley is another who is venting his frustration, warning that he will block the Rosenstein appointment unless the FBI answered questions.

South Carolina Senator Lindsey Graham is backing Grassley's threat to block Rosenstein.

Apparently the Justice Department sees itself in a no-win situation - if it denies that Trump was wire-tapped, it will be saying the president lied; and were it to confirm that there had been surveillance of Trump Tower, it would be confirming that very senior legal officers believed there was probable cause for a belief that Trump was acting as a foreign agent.

Frustrated that there has been no response to his demand, a week ago, for the FBI to produce copies of any warrants or court orders that would have sanctioned surveillance of Trump and his campaign, Graham also threatened to go the subpoena route, arguing on CNN: "I want to get to the bottom of it. The FBI would know if a warrant was issued, if a warrant was applied for. I want to answer that question."

Clearly of a belief that Trump has no evidence for his claim, Graham added: "Congress is gonna flex its muscle here, and you see that all over the place."

Trump has said little about his allegation since an early morning Twitter barrage on March 4 - and Spicer and other aides have only added to the confusion, even was they have attempted at times, to "walk back" Trump's allegation, arguing variously that Trump had not literally meant wire tap; that it could not comment in the midst of congressional investigations; that other remote surveillance techniques might have been used; and that the constitutional separation of powers prevented the disclosure of Trump's evidence.

In a Fox News interview on Wednesday evening, Trump confirmed conjecture that his claims of Obama wire-tapping him were based on media reports - and he was utterly confident that information would emerge in the coming days or weeks to vindicate him, which is to say that Trump was walking back the recent walk-back efforts by his aides.

Trump claimed he had "very good stuff" to offer on the subject and that he could speak in more detail on the subject as early as next week.

"Let's see whether or not I prove it," Trump said. "I just don't choose to do it right now."

Trump identified his source material as a January report in The New York Times on US investigators examining intercepted communications and financial transactions as part of a broad investigation into links between the Russian government and Trump officials - but the report said it wasn't clear the intercepted communications were connected to Trump or his campaign.

He also alluded, non-specifically, to a Fox News report.

Trump also qualified the claim in his "wire-tapping" tweet, claiming that what he had meant to say was to allege more generally that the Obama administration had engaged in "surveillance and many other things".