The caravan of more than 7,000 Central American migrants continues its journey in spite of exhaustion, heat, hunger and opposition from Mexican border police. But if the thousands of migrants reach the U.S. border, a new world of problems could await them.

This is the largest known caravan of migrants to head toward the U.S. border under the Trump administration. It's unclear how many of the migrants hope to ultimately enter the U.S. or exactly what would happen upon their arrival. But the administration's severe policies so far on immigration — along with President Trump's threats to stop the caravan — give an idea of what the migrants can expect.

Their arrival at the border would only begin another arduous journey, one that seems unlikely to end with many of them obtaining asylum.

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How the U.S. government would likely respond

For the best idea of what the U.S. government would do, consider what happened when a caravan of about 1,500 Central American migrants reached the U.S.-Mexico border in April 2018.

Of those 1,500, only about 250 legally remain in the U.S. pending an immigration hearing, according to Pueblos sin Fronteras, a humanitarian aid organization for migrants. Only three have been granted asylum. Some of the other migrants who arrived were kept in detention or deported.

That caravan's arrival came around the time the Trump administration began its widely-condemned practice of separating migrant families at the border as part of a "zero tolerance" policy to deter illegal immigration. Since then, the administration has issued or proposed policies that will likely make the process even harder for the migrants traveling to the border now.

So the next group of migrants are likely to encounter one of two outcomes: Sluggish bureaucracy or hard-line enforcement.

"A lot of the migrants are expecting to apply for asylum and for asylum to be granted," Sarah Pierce, a policy analyst for the nonpartisan Migration Policy Institute in Washington, D.C., told CBS News. "In reality, we have an immigration regime on the southern border that is enforcement-first."

The asylum process is notoriously slow, even for migrants who arrive prepared to apply for it, and cases can sometimes take years to resolve. As part of the asylum process, applicants must pass what's called a "credible fear" test, convincing immigration officials that their lives would be in danger if they returned to their home countries.

But in June, U.S. Attorney General Jeff Sessions overturned an Obama-era policy and made it harder for asylum-seekers to claim gang violence, drug smuggling and domestic violence as credible fears. Applicants must now prove that they would face persecution based on their race, religion, nationality or political beliefs.

Data has not yet been released showing how that change has affected the number of successful asylum applicants. But it would almost certainly invalidate the claims of many applicants who pursued asylum to escape violence back home.

The Trump administration in July also proposed a "binary choice" policy for family separations, which would give detained immigrant parents a choice: They could either be detained with their children as their case is processed, or they could stay in custody while allowing their children to be released. Pierce called this proposal "Family Separation 2.0."

That program has not officially started, but Pierce said it's another sign of the dire options awaiting the caravan migrants.

"It's going to be really frantic," she said.

The Department of Homeland Security and U.S. Customs and Border Protection did not return requests for comment from CBS News.

What will President Trump do?

President Trump has lobbed a series of threats about what he'll do if the caravan hits the border, though he lacks the authority to carry out most of them.

He said he will turn away all migrants who don't apply for asylum in Mexico first, but the U.S. has no such arrangement with Mexico, and international laws stipulate the U.S. must at least allow migrants to submit an asylum application if they have a well-founded fear of persecution at home.

Sadly, it looks like Mexico’s Police and Military are unable to stop the Caravan heading to the Southern Border of the United States. Criminals and unknown Middle Easterners are mixed in. I have alerted Border Patrol and Military that this is a National Emergy. Must change laws! — Donald J. Trump (@realDonaldTrump) October 22, 2018

Mr. Trump also vowed to reduce or cut off foreign aid to Guatemala, Honduras and El Salvador, but he would need congressional approval to do so. Likewise, his threat to mobilize the U.S. military and shut down the entire southern border would require a congressional waiver, as well as declaring a state of emergency, and any closure would take an immediate hit on trade with Mexico.

Any of these actions could also backfire and lead to more migration, since they would only add to the political and economic problems driving so many people out of those Central American countries. The Trump administration has "already implemented the most draconian policies," Pierce observed, and yet those "did not deter" this caravan from coming anyway.

Instead, President Trump's most direct impact could be using the caravan for political leverage to help Republicans in the midterm elections. In his rallies over the past week, Trump has baselessly accused Democrats of somehow organizing the caravan. He has claimed gang members and Middle Easterners are lurking among the migrants, though he acknowledged, "There's no proof of anything." And he's used the caravan as a rallying cry for supporting Republicans and stricter immigration laws, including funding for his long-promised border wall.

He has repeatedly told crowds at his rallies, "This is the election of the caravan."