WASHINGTON — Eager to defend a prolonged government shutdown over his border wall, President Donald Trump is pretending that he’s holed up nonstop at the White House waiting for a deal with Democrats. He’s also rewriting history regarding his promise to make Mexico pay for the wall.

Trump says he hasn’t left the White House in “months,” including during the partial shutdown that began Dec. 22. Actually, he has ventured out numerous times — to the Mexico border just this past week, for instance — and will again on Monday to New Orleans.

Trump also is claiming that he didn’t mean it when he told crowds over and over that Mexico would put up money for the wall. It was always intended for Mexico to pay “indirectly,” he now says, an assertion contradicted by his words and his plan in the campaign.

The remarks capped a week in which he also spread misleading rhetoric about the 2016 election, the FBI investigation into his former personal attorney Michael Cohen, prescription drug prices and dire threats from the south.

Trump said the wall will “very quickly pay for itself” by reducing the U.S. drug problem, and pay for itself “many times over” by the benefits he predicts will accrue to the U.S. economy from an updated trade deal with Canada and Mexico. Mexico has refused to pay anything toward a U.S. wall.

A look at the claims:

STUCK AT THE WHITE HOUSE

TRUMP: “I haven’t actually left the White House in months. …And I’ve been here virtually every night, I guess every night other than one day I flew to Iraq and then to Germany to see our troops. …I’m not even sure I actually missed a night, per se. But basically, I’ve been here for many months in the White House.” — interview Saturday night with Fox News.

TRUMP: “I’m in the White House, waiting. The Democrats are everywhere but Washington as people await their pay.” — tweet Sunday.

THE FACTS: Trump has left the White House plenty of times in recent months.

Besides his trip to Iraq and Germany on Dec. 26-27, Trump traveled to the Mexican border town of McAllen, Texas, on Thursday. On Monday, he’s going to New Orleans to address the American Farm Bureau. He’s left the White House during the shutdown for meetings at Camp David and the Capitol.

Shortly before the shutdown began, he traveled to Philadelphia to watch the Army-Navy football game (Dec. 8), visited Kansas City for a law enforcement conference (Dec. 7), attended former President George H.W. Bush’s funeral at the Washington National Cathedral (Dec. 5), participated in the G-20 summit in Argentina in late November; and hosted “Make America Great Again” rallies in Mississippi with Senate candidate Cindy Hyde-Smith (Nov. 26). He hosted a dinner on Thanksgiving at his Mar-a-Lago resort in Florida.

CRIME

TRUMP: “The building of the Wall on the Southern Border will bring down the crime rate throughout the entire Country!” — tweet Sunday.

THE FACTS: His statement that people in the country illegally are a special menace to public safety is at odds with plentiful research.

Multiple studies from social scientists and the libertarian think tank Cato Institute have found that people in the U.S. illegally are less likely to commit crime than U.S. citizens, and legal immigrants are even less likely to do so.

A March study by the journal Criminology found “undocumented immigration does not increase violence.”

The study, which looked at the years 1990 through 2014, said states with bigger shares of such people have lower crime rates.

As well, a study in 2017 by Robert Adelman, a sociology professor at University of Buffalo, analyzed 40 years of crime data in 200 metropolitan areas and found that immigrants helped lower crime. New York City, for example, has the nation’s largest population of immigrants living in the country illegally — about 500,000 — and last year had only 289 murders among a total population of 8.5 million people, according to preliminary data. Those numbers mean a person’s odds of becoming a victim of homicide in tightly packed, diverse New York City were about the same as they were last year in Montana.

2016 ELECTION

TRUMP: “The fact is, I was obviously a good candidate. …I won everything I did, and I won, and I won easily — 306-223, I believe. And that’s a big difference in the college, in the Electoral College.” — interview Saturday night with Fox News Channel.

THE FACTS: Trump misstates the Electoral College vote in his 2016 presidential race against Democrat Hillary Clinton. The official count was 304 to 227, according to an Associated Press tally of the electoral votes in every state.

Nor did he “win everything” in the 2016 campaign. Clinton won the popular vote, receiving nearly 2.9 million more votes than Trump after racking up more lopsided victories in big states such as New York and California, according to election data compiled by AP. But she lost the presidency due to Trump’s winning margin in the Electoral College, which came after he narrowly won less populous Midwestern states including Michigan and Wisconsin.

COHEN

TRUMP: “They broke into his law firm.” — interview Saturday night with Fox News, referring to the FBI.

THE FACTS: It was not a break-in. The FBI executed a search warrant obtained from a judge in conducting the raid and seizing records on a variety of matters, among them a $130,000 payment made to porn actress Stormy Daniels by Trump’s lawyer, Cohen. Daniels alleged she had extramarital affairs with Trump, which the White House denies.

The application for the warrant was approved high in the Justice Department.

DRUG PRICES

TRUMP: “Drug prices declined in 2018, the first time in nearly half a century. During the first 19 months of my Administration, Americans saved $26 Billion on prescription drugs. Our policies to get cheaper generic drugs to market are working!” — tweet Friday.

THE FACTS: The evidence isn’t on his side. And administration policies announced last year and currently being completed don’t seem to have shifted a trend of rising prices.

A recent Associated Press analysis of prices for brand-name drugs found far more increases than cuts in the first seven months of 2018. The analysis found 96 price hikes for every price cut. The number of increases had slowed somewhat and were not quite as steep as in past years.

And prices continue to rise. Figures on U.S. prescription drug price changes compiled by health data company Elsevier also show that from Dec. 20 through Jan. 2, there were 1,179 product price changes. Of those, 30 were price cuts and the remaining 1,149 were price increases, with 328 of them between 9 percent and 10 percent. All but one of the rest were by lower percentages.

WALL CONSTRUCTION

TRUMP: “The Fake News Media keeps saying we haven’t built any NEW WALL. Below is a section just completed on the Border. Anti-climbing feature included. Very high, strong and beautiful! Also, many miles already renovated and in service!” — tweet Friday, showing a section of bollard wall.

THE FACTS: No new miles of barrier construction have been completed under Trump. Existing fencing has been replaced or strengthened in a few areas. It’s true that many miles of barrier are in service — about 650 miles or 1,050 kilometers of fencing — but that was done by previous administrations.

MEXICO AND THE WALL

TRUMP: “I do have a plan on the Shutdown. But to understand that plan you would have to understand the fact that I won the election, and I promised safety and security for the American people. Part of that promise was a Wall at the Southern Border. Elections have consequences!” — tweet Saturday.

THE FACTS: He also promised during the campaign that Mexico would pay for the border wall. Mexico has refused.

Trump notes that “elections have consequences,” referring to his 2016 election. But there was another election, in November, and the consequence of that is that Democrats now control the House and they refuse to give Trump money for a wall.

TRUMP: “I never meant they’re going to write out a check… . Mexico is paying for the wall indirectly. And when I said Mexico will pay for the wall, in front of thousands and thousands of people, obviously they’re not going to write a check.” — remarks Thursday.

THE FACTS: A Trump campaign policy paper envisaged an explicit payment from Mexico: “It’s an easy decision for Mexico: make a one-time payment of $5-10 billion,” the paper said.

The plan outlined various ways for Trump to compel Mexico to pay for the wall, such as by Washington cutting off billions of dollars in remittances sent back to Mexico by immigrants living in the U.S., or by recouping the money through trade tariffs or higher visa fees. None of that has happened.

Although his campaign left open the possibility that Mexico might somehow contribute to the cost indirectly, Trump roused his crowds with the straight-ahead promise: “I will have Mexico pay for that wall.”

“Who?” he asked his supporters. “Mexico,” they shouted.

Now he is saying his words were not meant to be taken literally.

TRUMP: “They’re paying for the wall in a great trade deal.” — remarks Thursday in Texas.

THE FACTS: Nothing in his trade agreement with Mexico and Canada would cover or refund the construction cost or require a payment from Mexico. Instead he is assuming a wide variety of economic benefits will come from the agreement that can’t be quantified or counted on. For example, he has said the deal will dissuade some U.S. companies from moving operations to Mexico and he credits that possibility as a payment by Mexico.

The trade deal preserves the existing liberalized environment of low or no tariffs among the U.S., Mexico and Canada, with certain improvements for each country. The deal has yet to be ratified in any member country and its chances of winning legislative approval are not assured.

OBAMA VIDEO

TRUMP: “President Obama, thank you for your great support — I have been saying this all along!” — tweet Thursday, accompanied by video of Obama speaking as president in 2014.

THE FACTS: Trump’s tweet is deceptive, linking to a video clip that shows Obama, as president, discussing “an actual humanitarian crisis on the border” — a surge of tens of thousands of unaccompanied children and youth, mostly from Central America, who tried to cross from Mexico in 2014. Obama’s remarks do not support Trump’s proposal for a border wall, which the former president has criticized, or endorse the path Trump is considering now: declaring a national emergency that might enable him to circumvent Congress and unilaterally spend money on wall.

Instead, Obama was asking Congress to approve an emergency appropriation to deal with the surge.

CRISIS?

TRUMP: “Tonight I am speaking to you because there is a growing humanitarian and security crisis at our southern border.” — address to the nation Tuesday.

THE FACTS: Few would dispute that a humanitarian crisis is unfolding. A sharp increase in the number of families at the border, mostly from Central America, coupled with the Trump administration’s hardline stance is overwhelming border resources, adding to backlogs in the asylum system and leaving migrants in abysmal conditions on the Mexican side.

READ MORE: Trump says there’s a ‘crisis’ at the border. Here’s what the data says

Trump, however, has been unable to convince Congress that the border poses a national security crisis. He has made a series of statements falsely claiming that terrorists are pouring in from Mexico, that a wall would choke off shipments of illicit drugs and that people who get into the U.S. illegally commit a disproportionate share of violent crime.

The number of border arrests — the leading gauge of how many people are trying to cross illegally — is actually one-quarter of what it was in 2000, dropping from 1.6 million then to 400,000 in 2018.

DEMOCRATS

TRUMP: “Democrats will not fund border security.” — remarks Tuesday.

THE FACTS: They just won’t fund it the way he wants. They have refused his demand for $5.7 billion to build part of a steel wall across the U.S.-Mexico border.

Democrats passed legislation the day they took control of the House that offered $1.3 billion for border security, including physical barriers and technology. Senate Democrats have approved similar funding year after year. Many Democrats backed 2006 legislation that has resulted in the construction of about 650 miles (1,050 kilometers) of border barrier. Many also supported failed legislation in 2013 that would have doubled the length of fencing and allowed immigrants living in the country illegally to apply for a provisional legal status if they paid a $500 fine and had no felony convictions.

DRUGS

TRUMP: “A big proportion of the drugs from, you know, that we have … in this country come through the border.” — interview Saturday night with Fox News Channel.

TRUMP: “We lose 300 Americans a week, 90% of which comes through the Southern Border. These numbers will be DRASTICALLY REDUCED if we have a Wall!” — tweet Thursday.

TRUMP: “Our southern border is a pipeline for vast quantities of illegal drugs, including meth, heroin, cocaine and fentanyl. Every week, 300 of our citizens are killed by heroin alone, 90 percent of which floods across from our southern border.” — remarks Tuesday.

THE FACTS: What he’s trying to say in the tweet Thursday is that a wall would stop most heroin from coming into the country and drastically reduce heroin deaths, which average about 300 per week. But the Drug Enforcement Administration says “only a small percentage” of heroin seized by U.S. authorities comes across on territory between land ports of entry. Most of it is smuggled through official border crossings.

The agency says the same is true of drugs generally. In a 2018 report, it said the most common trafficking technique by transnational criminal organizations is to hide drugs in passenger vehicles or tractor-trailers as they drive into the U.S. though land entry ports, where they are stopped and subject to inspection. They also employ buses, cargo trains and tunnels, the report says, citing other smuggling methods that also would not be choked off by a wall.

Trump recently said drug smugglers don’t use ports of entry, an assertion flatly contradicted by his drug enforcement personnel.

READ MORE: Trump says walls work. It’s much more complicated

Despite that disconnect, Trump went so far as to say: “The border wall would very quickly pay for itself. The cost of illegal drugs exceeds $500 billion a year, vastly more than the $5.7 billion we have requested from Congress.”

THE EX-PRESIDENTS

TRUMP on a border wall: “This should have been done by all of the presidents that preceded me. And they all know it. Some of them have told me that we should have done it.” — Rose Garden news conference Jan. 4.

THE FACTS: Three ex-presidents — Bill Clinton, Jimmy Carter and George W. Bush — denied discussing the wall with Trump; the fourth, Obama, declined to answer. His office sent past comments by Obama criticizing the wall, and the two have not spoken since the inauguration except for a quick exchange at President George H.W. Bush’s funeral. Said Carter: “I have not discussed the border wall with President Trump, and do not support him on the issue.”

IMMIGRANT COSTS/BENEFITS

TRUMP: “America proudly welcomes millions of lawful immigrants who enrich our society and contribute to our nation but all Americans are hurt by uncontrolled illegal migration. It strains public resources and drives down jobs and wages.” — remarks Tuesday.

THE FACTS: The U.S. is not experiencing “uncontrolled” illegal immigration. The debate is over whether the controls are strong enough.

As for the costs, a major academic study in 2016 by the National Academy of Sciences, Engineering and Medicine found the job impacts of immigration, when measured over at least 10 years, are very small. It found immigration — legal and illegal — is an overall benefit to long-term economic growth.

Some evidence suggests that skilled immigrants boost wages. Native-born Americans without a high-school degree are most likely to suffer.

The academy study said estimating fiscal impacts of immigration is complex. Young and old immigrants tend to drain government resources while working-age immigrants contribute.

TERRORISM

TRUMP: “We have terrorists coming through the southern border because they find that’s probably the easiest place to come through. They drive right in and they make a left.” — Rose Garden news conference Jan. 4.

SARAH HUCKABEE SANDERS, White House press secretary: “We know that roughly, nearly 4,000 known or suspected terrorists come into our country illegally, and we know that our most vulnerable point of entry is at our southern border.” — “Fox News Sunday” Jan. 6.

THE FACTS: If they’re driving “right in” through border crossings, no wall would stop them. But as to the broader point, U.S. officials have produced no evidence of a terrorist influx from Mexico.

Trump and some of his aides have misrepresented statistics on foreigners who were stopped globally by Customs and Border Protection because they were on a watch list. They have suggested or plainly stated that they were stopped coming from Mexico.

Sanders acknowledged later in the week: “I should have said 4,000 at all points of entry, not just at the southern border.”

Despite Trump’s portrayal of Mexico as a teeming portal for terrorists, the State Department issued a report in September finding “no credible evidence indicating that international terrorist groups have established bases in Mexico, worked with Mexican drug cartels or sent operatives via Mexico into the United States.”

It went on: “The U.S. southern border remains vulnerable to potential terrorist transit, although terrorist groups likely seek other means of trying to enter the United States.”

Associated Press writers Darlene Superville, Colleen Long, Jill Colvin, Catherine Lucey, Zeke Miller and Kevin Freking in Washington and Elliot Spagat in San Diego contributed to this report.