Trump’s exact wording was that, absent Democrats' agreeing to fund the wall, he would “be forced to close the Southern Border entirely.”

That’s not possible, said Leon Fresco, an immigration lawyer at Holland & Knight. First, Trump can’t lawfully stop U.S. citizens from reentering the country from Mexico, so there’s no scenario in which the border could be closed off completely.

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What about closing it to foreigners crossing legally with visas? If the president tried that, it would face the same legal scrutiny as his travel ban of people from certain Muslim-majority countries, which has ping-ponged through the court system. And he’d have an even tougher sell closing off the southern border to legal entry, because he tweeted that his motivation to close the border is for political leverage and not an imminent national security threat, Fresco said.

The same would be true if he tried to further limit entry for refugees seeking asylum. His efforts already to restrict the ability of immigrants to request asylum at the border was struck down by a federal judge in California last week.

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“He is generally frustrated he can’t stop illegal crossings by fiat. He can’t build a wall. He can’t turn off the asylum system,” said Andrew Selee, president of the Migration Policy Institute. “He has a mounting frustration — the one thing that was his central promise to his voters, and they haven’t found a way at it yet. Trump wants a quick fix, and there’s no quick fix.”

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The only way Trump could potentially shut down the border would be through trade. But certain statutes in the North American Free Trade Agreement restrict him from stopping commerce between Mexico and the United States without a national security concern. And even then it would be for a limited period of time.

The business community in the United States and Mexico are afraid that Trump could introduce trade barriers gradually. But doing so would be “suicidal,” because it would hurt U.S. manufacturers, Selee said.

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“His problem here is not with Mexico, it doesn’t get him anywhere with Democrats, and it really hurts American industry,” Selee said. “You have this picture of trying to threaten someone, but it’s like telling a kid, ‘I’m going to take away the toy from this other kid.’ "

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Trump could theoretically pull out of NAFTA and then stop allowing commerce over the border, but that would also invite legal challenges. Fresco said many people with businesses that rely on Mexican goods would sue.

“There is no actual governmental compelling interest that led to you being taken out of business,” he said. “It can’t be just because the president is angry.”

So, ultimately Trump’s threat is fairly empty. There’s very little he can do to shut down the border that would stand up legally.