Donald Trump’s unflinching antagonism toward illegal immigration has galvanized activists who have grown to mistrust politicians on the issue, even those who have claimed to be as committed to the cause as they are.

And yet, for some, there is one nagging question that the candidate seems content to let linger — whether Trump’s Slovenian-born wife followed the law when she moved to the United States.

“Let them go wild, let it simmer, and then let’s have a little news conference,” Trump said at a rally this week, describing his strategy for handling those asking about his wife.

Mark Krikorian, a leading activist against illegal immigration, does not want to let it simmer. He wants an answer.

“Immigration is a big issue, and she is going to be first lady,” Krikorian said. “It matters.”

At a rally in Fayetteville, N.C., Aug. 9, Republican presidential nominee Donald Trump said his wife immigrated to the United States legally and added that she will soon hold a news conference about it. (The Washington Post)

Years before he ran for the White House, Trump built his political brand by accusing President Obama of concealing his past. Trump called on Obama to release his college applications, transcripts and other records, asking how such a “terrible student” got into Ivy League schools. The business executive also demanded that Obama release his passport records and, most famously, his birth certificate, declaring in a video released before the 2012 election: “We know very little about our president.”

But Trump has ensured that Americans know relatively little about him.

[Eight documents Trump has turned down requests to release]

He has refused to release many of the same documents that he demanded from Obama, including college transcripts and passport records. He has shirked the decades-old tradition of major nominees releasing their tax returns and other documentation to prove their readiness and fitness for office. And he has yet to release records showing why he received a medical deferment during the Vietnam War and whether he has actually donated the millions of dollars he claims to have given to charity.

While Democratic presidential nominee Hillary Clinton has hit Trump on his tax returns, saying this week that he “refuses to do what every other presidential candidate in decades has done,” Trump allies feel that Clinton has her own vulnerabilities when it comes to secrecy. Republicans have alleged that Clinton deleted thousands of emails from her private server to conceal favors done by her State Department for donors to her family’s charitable foundation — a charge Clinton has denied. And conservatives have called on Clinton, 68, to release her full medical records, citing a 2012 fainting episode in which she suffered a concussion. Ben Carson, a neurosurgeon and former GOP candidate, told Fox News this week that the information is “critical” for voters.

But Trump, in building a wall around his records, is setting a new standard for secrecy for modern-day candidates.

All other major presidential nominees from both parties since 1976 have released their tax returns. Last summer, Clinton released returns from 2007 to 2014, and her campaign on Friday shared her 2015 return, as well as 10 years of returns from her running mate, Sen. Tim Kaine of Virginia.

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Trump’s lack of disclosure has left Americans to take his word for it when he brags about his wealth and charitable donations. In May, Trump filed a lengthy financial disclosure with federal regulators that claimed business had been booming at many of his properties. He issued a news release claiming to be worth $10 billion. But Trump provided no documentation to back up the claims.

The Trump campaign did not respond to a request for all of the documents mentioned in this story, nor did it respond to questions about why it was not releasing the records.

Trump’s approach reflects a calculation that weathering the criticism for withholding documents is more politically palatable than the scrutiny that would come from giving the information to Trump’s opponents and what his campaign sees as an unfair media.

“You give the New York Times 20,000 pages of tax returns, they will give you 20,000 pages of defamation of character,” said former House speaker Newt Gingrich, who has advised Trump and was on his running mate shortlist.

Trump and his campaign have said there is nothing for voters to learn from these sorts of documents and that calls for their release were manufactured by the media.

“The only people who want the tax returns are the people who want to defeat him,” Trump’s campaign chairman, Paul Manafort, said in May.

[Trump once revealed his income tax returns. They showed he didn’t pay a cent.]

Trump’s tax filings would provide details such as how much money Trump makes, how much he gives to charity and the extent to which he has benefited from special exemptions and credits to minimize his tax rate. The tax returns would also show what Trump declares as business expenses and whether he keeps foreign accounts.

Some details have trickled out, revealing that Trump has a history of shrinking his tax burden. According to filings, legal documents and other public records, he paid no federal income taxes for at least five years — 1978, 1979, 1984, 1991 and 1993. Tax analysts say it is possible that Trump has continued to pay little to no income taxes thanks to generous tax deductions, including real estate depreciation. In May, Trump said he fights “very hard to pay as little tax as possible.”

Before he was a candidate, Trump presented himself as a champion of disclosure, particularly when it came to tax returns.

In 2011, he said he would release his filings if Obama released his long-form birth certificate.

Ahead of the 2012 election, Trump criticized Republican presidential nominee Mitt Romney for delaying the release of his tax returns, saying, “It’s a great thing when you can show that you’ve been successful and that you’ve made a lot of money.” Romney ended up releasing two years of tax returns, leading to criticism of his relatively low tax rate — a result that Trump recently cited in explaining his own reasons for not releasing.

Romney has called Trump’s refusal to release his tax returns “disqualifying for a modern-day presidential nominee” and has speculated that Trump must be hiding a “bombshell of unusual size.”

In 2014, Trump said he would “absolutely” release the returns “if I decide to run for office.” In 2015, he said his disclosure was contingent on finding “out the true story on Hillary’s emails.”

In January, Trump said he was almost ready to disclose his “very big . . . very beautiful” returns. But a month later, Trump reversed course, citing ongoing Internal Revenue Service audits of several years of his taxes.

An IRS spokesman said that nothing, including an audit, “prevents individuals from sharing their own tax information.” And President Richard Nixon released his tax records while under audit.

Trump’s tax attorneys said in a letter that his tax returns since 2009 are being audited. His attorneys also said that returns from 2002 to 2008 were no longer being audited, yet Trump said he will not release them because “they’re all linked.”

“I would give absolutely nothing until the audit is over,” Trump’s special counsel, Michael Cohen, said on CNN on Thursday. “That’s my advice to Mr. Trump.”

Trump’s running mate, Indiana Gov. Mike Pence, has yet to release his tax returns. Trump’s campaign and aides to Pence did not respond to requests for the returns.

Trump has also declined to release his educational records from the University of Pennsylvania, where he graduated in 1968 with a bachelor’s degree and took undergraduate classes at the famed Wharton School, which was then called the Wharton School of Finance and Commerce.

Trump has claimed that he was a top student at the Ivy League institution, although his name does not appear on lists of academic honors from the time.

While in college, Trump received four student deferments from the Vietnam War draft, and Trump has said that he received a fifth one for medical reasons because he had bone spurs that he says cleared up on their own. Trump has not produced the letter that he says he received from his doctor at the time documenting the problem.

Trump, 70, has also not released his medical records. Instead, in December, Trump released a four-paragraph letter from his doctor stating that a recent medical examination “showed only positive results” but not providing documentation such as lab results.

The letter ends with the guarantee: “If elected, Mr. Trump, I can state unequivocally, will be the healthiest individual ever elected to the presidency.”

In July 2015, Clinton released a two-page letter from her doctor listing the results of several lab tests, including an electrocardiogram, cholesterol levels and cancer screening results.

In the past, a number of nominees have released their medical health records to prove that they are healthy and fit for the job. Sen. John McCain (Ariz.), who was 72 when he was the GOP’s 2008 nominee and had suffered years of health problems since his time as a Vietnam War prisoner of war, released more than a thousand pages of medical records.

The questions about Melania Trump’s immigration status have emerged in the wake of newly published nude photographs of the former model.

Melania Trump has said she came to the country in 1996 on a visa that allowed her to work, but the photos were taken in New York in 1995. She met Donald Trump in 1998, and they were married in 2005. She has said she got a green card in 2001 and became a citizen in 2006.

[Many questions and few answers about how Melania Trump immigrated to the U.S.]

“I follow a law the way it’s supposed to be,” she told MSNBC earlier this year. “I never thought to stay here without papers. I had visa.”

Paolo Zampolli, an Italian-born business executive based in New York who once owned modeling agencies, told The Washington Post last week that his agency, Metropolitan Models, sponsored Melania Trump, then Melania Knauss, for an H-1B work visa in 1996 after he spotted her while scouting models in Milan and Paris. Working models are eligible for an H-1B if they can show “distinguished merit or ability” in their field. Zampolli said Knauss qualified based on her past work as a model in Europe.

The campaign has not responded to requests for documentation to back up the account, or to explain the process through which Trump received her green card. And it is not clear when, or if, the campaign will schedule the news conference that Donald Trump mentioned this week.

“Let me set the record straight,” Melania Trump tweeted last week. “I have at all times been in full compliance with the immigration laws of this country. Period.”

Drew Harwell, Mary Jordan, Abby Phillip and Karen Tumulty contributed to this report.