(CNN) President Donald Trump's refusal to let sleeping dogs lie now threatens to harm his presidency.

His revival of debunked claims that millions of illegal voters are to blame for him losing the popular vote to Hillary Clinton and call for a major investigation -- in essence challenging the legitimacy of his election -- is in danger of overshadowing the otherwise fast start he has made in honoring campaign promises and changing America.

In two tweets, Trump on Tuesday said : "I will be asking for a major investigation into VOTER FRAUD, including those registered to vote in two states, those who are illegal and.... even, those registered to vote who are dead (and many for a long time). Depending on results, we will strengthen up voting procedures!"

Trump first made his claims about illegal voters after it became clear soon after November's election that he would lose the popular vote but win the electoral college. His revived the charge in a meeting with congressional leaders on Monday night.

I will be asking for a major investigation into VOTER FRAUD, including those registered to vote in two states, those who are illegal and....

His spokesman, Sean Spicer, was unable to quell the controversy on Tuesday, citing "studies and evidence" as the basis for Trump's claims -- then refused to discuss or produce any such material.

"The President does believe that, I think he's stated that before, and stated his concern of voter fraud and people voting illegally during the campaign and continues to maintain that belief based on studies and evidence people have brought to him," Spicer said.

The reappearance of a controversy the Trump camp had thought was in the past was another sign of one of the President's most dominant traits -- an inability to accept any suggestion that he was unable to pull off a complete and total victory in any area of his life.

The self-ignited controversies in the first five days of his presidency -- including one about the size of his inaugural crowds -- also hints at a deeper and consuming need to be demonstrated as legitimate that has driven Trump for decades and has sometimes been an Achilles heel.

As so often, the steps Trump takes to try to satisfy his craving for respect and to be seen as a spectacular victor threaten to make that recognition ever more elusive.

In this case, his refusal to accept that he lost the popular vote fair and square, despite winning the electoral college and the presidency, threatens to detract from another far more significant story -- his sweeping use of executive power to live up to campaign promises and begin to change America.

JUST WATCHED Donald Trump withdraws from TPP Replay More Videos ... MUST WATCH Donald Trump withdraws from TPP 02:46

He has moved to revive the Keystone XL and Dakota Access oil pipelines, killed the Trans-Pacific Partnership and begun the process of taking apart Obamacare.

Next week, Trump is expected to name a Supreme Court nominee, a potential legacy-making opportunity most presidents don't get in their first week in office.

But the revived debate about voter fraud is a sign that the off-the-cuff controversies that Trump used to his political benefit during the campaign have the capacity to actually damage him as President because they undermine the trust that is a vital commodity for every commander in chief.

A number of academic and governmental studies have found no evidence of voter fraud to back up what would be the most sensational story election in American history.

Trump's deep desire for legitimacy is not some new character trait that has emerged from during his early days in power.

Throughout his campaign, his obsession with polls, boasts about his wealth, lavish praise for his buildings and business revealed a candidate unusually open to talking up his achievements and place in the world.

Michael D'Antonio, author of a recent book "The Truth About Trump" said the President's obsessive desire for recognition was on display through his long climb to prominence as a business tycoon.

"He absolutely has done this for his entire life -- going back to childhood when he had to tell people he was the best baseball player in New York state when baseball is something they keep records on and they can prove it's not true. He was raised by a very demanding father and his father did not tolerate anything but complete victory and success in everything that Donald did."

But now, Trump has finally arrived at a position where the scrutiny is intense and claims and boasts that could be put down to the braggadocio of a real estate tycoon in the business world no longer fly.

"This is the first time in his life that he has to play by rules that other people establish ... (but) he doesn't see any difference between salesmanship and being a president," said D'Antonio, also author of a new book about Barack Obama called "A Consequential President."

The most remarkable aspect of Trump's desire for recognition is that while there are millions of Americans who would never vote Republican or who were appalled by Trump's behavior on the campaign trail, official Washington has accepted him as President with little reservation. Even Bill and Hillary Clinton made a point of attending his inauguration Friday.

Notwithstanding his searing condemnation of the city's political elites in his inaugural address, congressional leaders have already traveled to the White House to yuck it up with the new President. Republicans are consulting him as they lay out a legislative schedule. Democrats, as is normal for an opposition party shut out of power, are plotting their resistance.

Photos: Donald Trump's Inauguration Day President Donald Trump, flanked by Vice President Mike Pence and Chief of Staff Reince Priebus, signs his first executive order on health care, Friday, January 20, in the Oval Office of the White House in Washington. Hide Caption 1 of 48 Photos: Donald Trump's Inauguration Day President Donald Trump smiles with his son Barron as they watch the 58th Presidential Inaugural Parade in Washington on Friday, January 20. Hide Caption 2 of 48 Photos: Donald Trump's Inauguration Day President Donald Trump salutes members of the New York Military Academy during the 58th Presidential Inaugural Parade on Friday, January 20. Hide Caption 3 of 48 Photos: Donald Trump's Inauguration Day President Donald Trump and Vice President Mike Pence salute military personnel from the main reviewing stand in front of the White House during the Presidential Inaugural Parade. Hide Caption 4 of 48 Photos: Donald Trump's Inauguration Day President Donald Trump steps out of his limousine in front of the Presidential Inaugural Parade reviewing stand on Pennsylvania Avenue on Friday, January 20. Hide Caption 5 of 48 Photos: Donald Trump's Inauguration Day Vice President Mike Pence, center, waves to supporters as he walks with his family during the Presidential Inaugural Parade. Hide Caption 6 of 48 Photos: Donald Trump's Inauguration Day Spectators watch from rooftops as President Donald Trump and first lady Melania Trump walk in the inaugural parade on Friday, January 20, in Washington. Hide Caption 7 of 48 Photos: Donald Trump's Inauguration Day President Donald Trump waves as he walks on Pennsylvania Avenue with first lady Melania Trump during the Presidential Inaugural Parade on Friday, January 20. Hide Caption 8 of 48 Photos: Donald Trump's Inauguration Day The U.S. Army Old Guard Fife and Drum Corps marches in the Presidential Inaugural Parade on Friday, January 20, in Washington. Hide Caption 9 of 48 Photos: Donald Trump's Inauguration Day Secret Service members surround the presidential limousine as it drives up Pennsylvania Avenue during the Presidential Inaugural Parade on Friday, January 20, in Washington. Hide Caption 10 of 48 Photos: Donald Trump's Inauguration Day Police escorts participate in the Presidential Inaugural Parade procession on January 20, in Washington. Hide Caption 11 of 48 Photos: Donald Trump's Inauguration Day From left, first lady Melania Trump, President Donald Trump, US Army Maj. Gen. Bradley Becker, Vice President Mike Pence and Karen Pence review the troops as part of the inaugural ceremonies. Hide Caption 12 of 48 Photos: Donald Trump's Inauguration Day Members of a military band line up prior to marching in the Presidential Inaugural Parade. Hide Caption 13 of 48 Photos: Donald Trump's Inauguration Day President Trump waves to Hillary Clinton, whom he defeated in the election, during his speech at the inaugural luncheon. He was sworn in as the 45th President of the United States on Friday, January 20. Hide Caption 14 of 48 Photos: Donald Trump's Inauguration Day Dignitaries bow their heads in prayer during the inaugural luncheon. Hide Caption 15 of 48 Photos: Donald Trump's Inauguration Day Newly sworn in President Trump shakes hands with Hillary Clinton. Hide Caption 16 of 48 Photos: Donald Trump's Inauguration Day President Trump is joined by the congressional leadership and his family as he formally signs his cabinet nominations into law. Hide Caption 17 of 48 Photos: Donald Trump's Inauguration Day Former President Barack Obama waves as he boards a Marine helicopter during a departure ceremony. Hide Caption 18 of 48 Photos: Donald Trump's Inauguration Day The Obamas and Trumps walk to Marine One after Donald Trump was sworn in as President. Hide Caption 19 of 48 Photos: Donald Trump's Inauguration Day President Trump delivers his inaugural address after being sworn in as the 45th President of the United States on Friday, January 20. Hide Caption 20 of 48 Photos: Donald Trump's Inauguration Day Trump is sworn in as President with his wife, Melania, at his side. Hide Caption 21 of 48 Photos: Donald Trump's Inauguration Day Supporters watch as Trump appears for his inauguration. Hide Caption 22 of 48 Photos: Donald Trump's Inauguration Day Vice President Mike Pence is sworn in by Justice Clarence Thomas as Pence's wife, Karen, holds the bible. Hide Caption 23 of 48 Photos: Donald Trump's Inauguration Day Trump arrives on the West Front of the Capitol to be sworn in. Hide Caption 24 of 48 Photos: Donald Trump's Inauguration Day President Barack Obama chats with Trump before the ceremony. Hide Caption 25 of 48 Photos: Donald Trump's Inauguration Day Trump arrives on the West Front of the Capitol. Hide Caption 26 of 48 Photos: Donald Trump's Inauguration Day Trump waits to step out onto the portico for his presidential inauguration. Hide Caption 27 of 48 Photos: Donald Trump's Inauguration Day Pence arrives at the Capitol for the inauguration. Hide Caption 28 of 48 Photos: Donald Trump's Inauguration Day Obama and Vice President Joe Biden arrive on the West Front of the Capitol. Senate Minority Leader Chuck Schumer and House Minority Leader Nancy Pelosi step before them. Hide Caption 29 of 48 Photos: Donald Trump's Inauguration Day Melania Trump arrives for the ceremony. Hide Caption 30 of 48 Photos: Donald Trump's Inauguration Day Former President Jimmy Carter, Rosalynn Carter, former President Bill Clinton, Hillary Clinton, former President George W. Bush and Laura Bush wait for the ceremony to begin. Hide Caption 31 of 48 Photos: Donald Trump's Inauguration Day Trump's children look for their seats before the ceremony begins. Hide Caption 32 of 48 Photos: Donald Trump's Inauguration Day Supreme Court justices await the ceremony. Front from left: Chief Justice John Roberts and Justices Anthony Kennedy and Clarence Thomas. Back from left: Justices Ruth Bader Ginsburg, Sonia Sotomayor, Stephen Breyer and Samuel Alito. Hide Caption 33 of 48 Photos: Donald Trump's Inauguration Day Crowds file in along the National Mall before Trump's swearing-in. Hide Caption 34 of 48 Photos: Donald Trump's Inauguration Day Former House Speakers Newt Gingrich and John Boehner arrive with their wives at the Capitol. Hide Caption 35 of 48 Photos: Donald Trump's Inauguration Day Former Vice President Dick Cheney arrives for the inauguration. Hide Caption 36 of 48 Photos: Donald Trump's Inauguration Day Sen. Ted Cruz arrives for the ceremony. Hide Caption 37 of 48 Photos: Donald Trump's Inauguration Day Sen. Bernie Sanders waves to the crowd from the West Front of the Capitol before the ceremony. Hide Caption 38 of 48 Photos: Donald Trump's Inauguration Day The presidential motorcade moves down Pennsylvania Avenue to the Capitol for the inauguration ceremony. Hide Caption 39 of 48 Photos: Donald Trump's Inauguration Day Former Vice President Dan Quayle and his wife, Marilyn, arrive for the ceremony. Hide Caption 40 of 48 Photos: Donald Trump's Inauguration Day The Obamas welcome the Trumps to the White House as they arrive for inauguration festivities Hide Caption 41 of 48 Photos: Donald Trump's Inauguration Day President Obama kisses the first lady as they await the arrival of President-elect Trump and his wife, Melania. Hide Caption 42 of 48 Photos: Donald Trump's Inauguration Day Pence arrives for a worship service at St. John's Episcopal Church across from the White House. Hide Caption 43 of 48 Photos: Donald Trump's Inauguration Day The Rev. Luis Leon greets the Trumps on their arrival for the service at St. John's. Hide Caption 44 of 48 Photos: Donald Trump's Inauguration Day The rain doesn't deter a crowd from gathering to watch the inauguration ceremony. Hide Caption 45 of 48 Photos: Donald Trump's Inauguration Day Workers dry seats on the West Front of the US Capitol. Hide Caption 46 of 48 Photos: Donald Trump's Inauguration Day Vice President Joe Biden and his wife, Jill, prepare to leave the White House for the final time. Hide Caption 47 of 48 Photos: Donald Trump's Inauguration Day The sun begins to rise behind the Capitol as Washington prepares for Donald Trump's inauguration. Hide Caption 48 of 48

President frustrated by coverage

But Trump seems unable to turn the other cheek -- even before his inauguration he launched into a Twitter tirade against Democratic Rep. John Lewis who had said he was not a legitimate President, instead of taking the politically wiser course of just shrugging off the revered congressman's jab.

Spicer offered a revealing glimpse into the President's psyche during his first briefing on Monday, prompted by a question from CNN's Jim Acosta.

JUST WATCHED John Lewis: Trump not a 'legitimate' president Replay More Videos ... MUST WATCH John Lewis: Trump not a 'legitimate' president 02:10

"There is this constant theme to undercut the enormous support that he has," Spicer said. "And I think that it's just unbelievably frustrating when you're continually told it's not big enough, it's not good enough, you can't win."

Spicer said that Trump had not been taken seriously when he started to run for president and had constantly been told that he would lose.

"He's gone out there and defied the odds over and over and over again. And he keeps getting told what he can't do by this narrative that's out there," Spicer said, in remarkably candid comments for a presidential spokesman.

"And he exceeds it every single time. And I think there's an overall frustration when you turn on the television over and over again and get told that there's this narrative that you didn't win."

While those sentiments may accurately reflect opinion in Trump's inner circle, they do not take into account that Trump's preoccupation with triviality could become a liability for his administration.

He's already triggered a furious backlash on Capitol Hill after repeating his conspiracy theory about his failure to win the popular vote in front of congressional leaders on Monday, according to several sources.

"If the President of the United States is claiming that 3.5 million people voted illegally, that shakes confidence in our democracy -- he needs to disclose why he believes that," Republican Sen. Lindsey Graham told CNN on Tuesday.

Rep. Will Hurd, a Texas Republican, said he saw no evidence of widespread voter fraud.

"I would suggest the White House looks in their windshield and not the rearview mirror. They did something that nobody thought they could do. They should be proud (of) that and not let this be a distraction," Hurd told CNN's Wolf Blitzer on "The Situation Room."

There are also longer term implications for Trump's failure to develop a thicker skin.

His White House will face far more political pressure and unflattering press coverage in the future than it does now.

There will be times when it feels the Oval Office is the most isolated place in the entire world. The most successful presidents are those who can still function under that intense scrutiny. And the most capable White House staffs help a president maintain the credibility and trust that he must call upon in times of crisis — whatever his press clippings say.

Trump not alone

Still, as he fends of criticism over his comments, Trump can console himself that he is not alone in experiencing intense frustration over his press coverage and feeling he is not getting his due as President.

After winning a landslide in 1964, Lyndon Johnson complained that journalists were criticizing him as having no rapport with voters or saying he was just the beneficiary of fighting against a weak Republican candidate in Barry Goldwater.

In comments strikingly similar to Trump's, LBJ told his adviser Edwin Weisl in a telephone call: "I had the biggest crowd they ever had before and I got the biggest vote anybody ever got before. I had the greatest affection that had ever been demonstrated," Johnson said.

"But they say 'Aw-w-w-w, that doesn't amount to anything," Johnson said, in a transcript of the call included in the book "Reaching for Glory" by Michael Beschloss.

Soon after his inauguration in 1993, Bill Clinton complained that he had never really had a "honeymoon" with the press which he thought was more interested in sensational leaks than substantive politics," according to the Taylor Branch's book "The Clinton Tapes."

Still, Clinton and LBJ did not take the same approach as Trump — who blared out his anger publicly — instead leaving it to history to reveal their fury.