There are two ways to look at the crazed Twitter storm early on Saturday, in which the US President accused former president Barack Obama of criminally ordering wiretaps on Trump Tower.

Were the tweets an after-the-fact distraction from Attorney-General Jeff Sessions complicating Trump's Russia nightmare, with his failure to disclose his meetings with the Russian ambassador and then his embarrassing recusal from any Justice Department deliberations on the various Russian-links inquiries; or was this a pre-emptive smokescreen for the shortcomings of Trump's revised executive order on migration, released on Monday morning?

Or did Trump's bout of tweeted rage serve to shine a light on a little-noticed body of evidence on the Trump campaign's Russian connections that warrants further investigation, because any request by the security agencies for court approval for the kind of surveillance alleged by Trump required it to produce a body of believable evidence?

The fallout needs to be unpacked in parts. But first, that new executive order.

Monday's unveiling was very different to that of its predecessor. For starters, the TV cameras were not wheeled in to record Trump fixing his signature to the new document and, despite Trump's protests about unnamed sources, the administration officials who explained the document in media briefings insisted that their names not be published.

And despite claims by the administration, the new document has its problems.

Iraq has been removed from the original list of seven countries from which travellers have been banned, which is interesting, given that it is a global hotbed of terrorism. But none of the other hotbed countries in the Middle East or elsewhere in the world has been added.

In an attempt to counter a key criticism of the original order - that citizens of the banned countries had not been involved in terror strikes in the US - the administration sought to firm up the national security justification for the order by claiming that 300 people who had entered the US as refugees were the subject of counter-terrorism investigations, but it refused to disclose their nationalities.

In any event, The Washington Post reports that a Homeland Security report on the terrorist threat posed by people from the seven countries has concluded that citizenship was an "unreliable" threat indicator and that people from the affected countries have rarely been implicated in US-based terrorism.

Also, the new order does nothing to quash the claim by former New York mayor and Trump surrogate Rudy Giuliani that Trump had asked him to take the "Muslim ban" that candidate Trump had called for and to "show me the right way to do it legally".

But back to the Trump tweets.

In tweeting as he did on Saturday, Trump has created an unprecedented circumstance - FBI director James Comey is effectively calling him a liar; Trump's Republican colleagues in Congress are not rushing to support him; and even his loyal staffers are choosing their words carefully.

"I think he firmly believes that this is a story," spokeswoman Sarah Huckabee Sanders said in one interview, and in another: "Look, I think he's going off information that he's seen that has led him to believe that this is a very real potential."

Another problem is that, if or when Trump is proved wrong, he'll look like a bit of a dill. In the event that it's proved that a wiretapping court order was issued, in all probability without Obama's knowledge, it would mean that a federal court had been convinced there were genuine reasons of national security for such an order - on which, more later.

The torrent of leaks driving Trump nuts continues.

In assembling a remarkable portrait of Trump as "mad - steaming, raging mad" on the weekend, The Washington Post had co-operation from no less than 17 White House officials and others in Trump's circle. One went on the record: "He was pissed. I haven't seen him this angry," his friend and Newsmax chief executive Christopher Ruddy said of two weekend encounters with the President.

Gnawing at Trump, apparently, is the then-and-now comparison - at this stage of the Obama presidency, Obama seemingly was getting things done.

Even Trump thought as much at the time, saying of Obama's first press conference in February 2009: "First of all, I thought he did a great job tonight. I thought he was strong and smart, and it looks like we have somebody that knows what he is doing finally in office, and he did inherit a tremendous problem. He really stepped into a mess."

Each week is supposed to be a reboot for Trump. Last week his well-received address to the joint houses of Congress was supposed to be a fresh start, but it was bombed out of the water by reports on the Sessions meeting with ambassador Sergey Kislyak. This week too was to be a reboot, with the new migration executive order and a promised definitive plan to "repeal and replace" Obamacare - but Trump's weekend tweets are keeping Russia on the boil.

All is not well in Trumpworld.

Apparently Trump's newly minted Health and Human Services Secretary Tom Price has been deemed incapable of selling the death of Obamacare and the birth of whatever is to replace it - so Trump has given the task to Mick Mulvaney, director of the Office of Management and Budget.

And Sessions is in hot water too - for revealing his meetings with the ambassador in answer to a question during his confirmation hearing that didn't ask if he had any such meetings.

The whole White House gang reportedly is furious with the Attorney-General's stumbles and Trump, in particular, is fuming that Sessions caved to demands that he recuse himself without consulting the White House, as various aspects of Trump's Russian links which are being investigated by several of the intelligence agencies that Trump so loathes and by five congressional committees.

The Post's portrait of Trump's tantrums: "[He] simmered with rage... He upbraided [his advisers] over Sessions' decision to recuse himself, believing that Sessions had succumbed to pressure ???"

The New York Times had more: "[He] railed at aides about the recusal, singling out the White House counsel's office and the communications staff in a tirade visible through the window to a nearby television camera."

The leaks are not to be underestimated as a cause of presidential anger. Republican congressman and chairman of the House Intelligence Committee Devin Nunes told the Post: "It's not paranoia at all when it's actually happening. It's leak after leak after leak from the bureaucrats in the [intelligence community] and former Obama administration officials - and it's very real.

"The White House is absolutely concerned and is trying to figure out a systemic way to address what's happening."

The FBI's Comey is being circumspect - his dismissal of Trump's charge against Obama is being sourced to unnamed officials. But James Clapper, a former director of national intelligence, didn't beat around the bush.

Asked if a secret intelligence warrant had been issued, Clapper bluntly told NBC's Meet the Press: "Not to my knowledge, no. There was no such wiretap activity mounted against the president-elect at the time, as a candidate or against his campaign."

Had there been such an order or an application for one, Clapper insisted that he would "absolutely" have been informed of it. "I can deny it," he said.

Asked to substantiate the Trump tweets, the White House cited a selection of news reports from the BBC and Heatstreet in Britain and The New York Times and Fox News in the US, all of which touch on an aspect of the Russia investigations.

An analysis by the Cato Institute's Julian Sanchez says: "The allegation made by various news sources is that, in connection with a multi-agency intelligence investigation of Russian interference with the presidential election, the FBI sought an order from the Foreign Intelligence Surveillance Court authorising them to monitor transactions between two Russian banks and four persons connected with the Trump campaign ???

"[But] there's nothing here to suggest either the direct involvement of President Obama nor any clear indication of a violation of the law."

The Cato analysis then summarises a Breitbart News report that reportedly was critical in winding up the Trump Twitter storm - "the Obama administration sought, and eventually obtained, authorisation to eavesdrop on the Trump campaign; continued monitoring the Trump team even when no evidence of wrongdoing was found; then relaxed the NSA rules to allow evidence to be shared widely within the government, virtually ensuring that the information, including the conversations of private citizens, would be leaked to the media".

It then concludes: "None of this is really supported by the public record ??? In short, both Breitbart and Trump have advanced claims far more dramatic than anything the public evidence can support".

Awarding Trump four Pinocchios, the Post's fact-checker Glenn Kessler writes: "Only two articles, both with British roots, have reported that a FISA court order was granted in October to examine possible activity between two Russian banks and a computer server in the Trump Tower. This claim has not been confirmed by any US news organisations.

"Moreover, neither article says President Obama requested the order or that it resulted in the tapping of Trump's phone lines. We're still waiting for the evidence ???"

So, executive orders will come and go, but the Russia mess remains and Trump's soundness of mind continues to be questioned - even in Republican circles.

"We have as president a man who is erratic, vindictive, volatile, obsessive, a chronic liar, and prone to believe in conspiracy theories," conservative commentator and former George W. Bush policy chief Peter Wehner told the Post. "And you can count on the fact that there will be more to come, since when people like Donald Trump gain power they become less, not more, restrained".

On the weekend White House spokesman Sean Spicer pushed back on reporters' demands for more detail on Trump's attack on Obama: "If we start down the rabbit hole of discussing this stuff, we end up in a very difficult place."

As my old colleague Tommy Taylor would say: "Too right, Sean. You sprayed a bib-full."