Washington (CNN) President Donald Trump and his allies have launched a full-court press to convince Americans, and skeptical lawmakers, that there is a crisis on the Southern border, and the only way to fix it is to approve billions of dollars for Trump's signature border wall.

But senior Trump administration officials, including Vice President Mike Pence and Homeland Security Secretary Kirstjen Nielsen, have relied on misleading statements to make their case. Trump, who is also prone to repeating debunked talking points about immigration, is set to deliver his Oval Office address about the topic on Tuesday night.

Here's a breakdown of the most recent misleading claims, the half-truths and everything in between, along with the fuller picture, based on official statistics and reporting from CNN.

Illegal border-crossings

In each of his three television interviews Tuesday morning, Pence led his argument that there is a crisis on the southern border with one figure: 60,000.

"60,000 people are now attempting to come into our country illegally every month," Pence said in his interview with NBC , a claim he echoed on CBS and ABC.

Pence's use of that statistic is misleading at best because it gives the impression that 60,000 people are caught trying to sneak in every month. He is lumping in people who presented themselves at ports of entry in addition to those who were apprehended illegally crossing the border.

Official statistics from Customs and Border Protection (CBP) tell the fuller story.

Of the 62,456 individuals who were apprehended or deemed inadmissible at the southern border in November, 10,600 presented themselves at legal US ports of entry and were ultimately deemed inadmissible. Same goes for the 60,722 figure for October. It includes 9,771 who showed up at legal US ports of entry and were subsequently deemed inadmissible into the country.

The Trump administration has repeatedly pointed to these figures, the most recent available, to back up its claim that there is a border crisis. But while border apprehensions increased in those months, they didn't surge in an unprecedented fashion as the administration is claiming.

Even including the number of individuals denied admission at designated ports of entry, there were comparable increases and decreases in previous years. The numbers surged to similar levels in late 2016 only to drop again in early 2017, according to CBP numbers.

Terrorists entering the US from Mexico

For months, Trump has raised the specter of "terrorists" crossing the US-Mexico border. He brought this up repeatedly before the 2018 midterms when a caravan of migrants, primarily from impoverished Central American countries, marched through Mexico toward the US border.

These claims were debunked at the time as exaggerations and speculation. Though they've made a comeback this year. White House press secretary Sarah Sanders was fact-checked live on Fox News when she said Sunday "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."

Nielsen tried to massage the narrative with a series of tweets on Monday: "The number of terror-watchlisted encountered at our Southern Border has increased over the last two years. The exact number is sensitive and details about these cases are extremely sensitive."

Recent reporting revealed that the actual number encountered on the southern border is nowhere near the staggering 4,000 figure. An administration official told CNN that only about a dozen non-citizens on the terrorism watch list who were stopped at the US-Mexico border in fiscal year 2018. That is a tiny fraction of all known or suspected terrorists who tried to enter or travel to the US in that timeframe.

Additionally, a State Department report from 2016 said there was "no credible information that any member of a terrorist group has traveled through Mexico" to sneak into the United States.

"I cannot think of a single example of a terrorism case where somebody came over the southern border to infiltrate the United States," said Peter Bergen, a CNN national security analyst who has tracked hundreds of terrorism cases. "It's sort of a non-problem."

Bergen noted that the most notorious case of a terrorist apprehended at the US border is the "millennium plot," when an Algerian citizen with ties to al-Qaeda was arrested at the US-Canada border in December 1999. He hoped to blow up Los Angeles International Airport.

'Special interest alien' semantics

In a fact sheet released Monday, DHS reiterated claims that last year, the agency "encountered more than 3,000 'special interest aliens'" at the southern border. Nielsen touted this number last week from the Rose Garden after Trump publicly pressed lawmakers to fund his wall proposal.

"They either have travel patterns that are identified as terrorist travel patterns or they have known or suspected ties to terrorism," Nielsen said, describing the "special interest alien" term.

There's no uniform definition of the term " special interest alien ," but DHS defines a "special interest alien" as a non-US person "who, based on an analysis of travel patterns, potentially pose a national security risk to the United States or its interests." Someone might be flagged for additional vetting because of where they're traveling from or how they arrived in the US.

That doesn't mean, however, that all "special interest aliens" are terrorists, according to DHS.

In an interview with CNN, David Bier, an immigration policy analyst at the Cato Institute, explained that a Syrian Christian who asks for asylum, for example, would be classified as a "special interest alien" simply because he/she is from Syria. According to a report from the libertarian think tank, no "special interest alien" has produced a terrorist attack on US soil.

Drugs coming across the border

The influx of illegal drugs is another key element of the Trump administration's case for building a wall to address what they describe as a crisis at the border. Pence said Tuesday that "90% of all the heroin that comes into this country, that claims the lives of 300 Americans every week, comes through our southern border."

Similarly, a DHS presentation to lawmakers last week claimed that there was "a dramatic spike in illegal drugs at the southern border" and that this justified the urgent need to build a wall.

The majority of hard narcotics seized by Customs and Border Protection come through ports of entry either in packages, cargo or with people who attempt to enter the US legally. The only drug that is smuggled in higher numbers between legal entry points is marijuana, according to information from Customs and Border Protection and the Drug Enforcement Administration.

For example, the majority of the heroin flow on the southern border into the US is through privately owned vehicles at legal ports of entry, followed by tractor-trailers, where the heroin is co-mingled with legal goods, according to the DEA's 2018 annual drug threat assessment

The DHS presentation said there was a 38% increase in methamphetamine at the southern border from 2017 to 2018. There was an increase in both methamphetamine and fentanyl seizures at both ports of entry and between the legal entry points over the past year, but the percentage is unclear since data for the last month of fiscal year 2018 is unavailable.

A closer look at the numbers shows that in fiscal year 2018, Customs and Border Protection seized 67,292 pounds of methamphetamine at legal ports of entry, compared with 10,382 pounds by Border Patrol agents in between ports, based on available data.