(CNN) Thousands of migrants are about to arrive at Mexico's doorstep. And US Secretary of State Mike Pompeo is meeting with officials in Mexico's capital to discuss the situation.

The Honduran migrants, trekking in a caravan toward Mexico's southern border , say they're heading for the United States -- fleeing violence and searching for economic opportunity.

Pompeo, meanwhile, is heading into meetings in Mexico City with a message for leaders there about the massive caravan of migrants: Stop them before they reach the US border.

The key questions: Will Mexico let the migrants in? And what will happen if they do?

The crossing point

The caravan quickly grabbed the attention of world leaders as word of its formation spread over the weekend. By Tuesday, US President Donald Trump had weighed in with a warning, threatening to cut foreign aid to Honduras if the group didn't turn back.

But government statements, Twitter posts and even a police blockade haven't succeeded in stopping the caravan. Thousands of Honduran migrants are traveling through Guatemala, according to humanitarian aid groups. And hundreds more are traveling through El Salvador en route to Guatemala.

Photos: The caravan's journey, in photos Migrants heading in a caravan to the United States rest on a basketball court in San Pedro Tapanatepec, Mexico. on Sunday, October 28. Hide Caption 1 of 60 Photos: The caravan's journey, in photos Migrants rest on a road between the Mexican states of Chiapas and Oaxaca after federal police briefly blocked them outside the town of Arriaga on Saturday, October 27. Hide Caption 2 of 60 Photos: The caravan's journey, in photos The caravan comes to a standstill after police block it outside Arriaga on Saturday. Hide Caption 3 of 60 Photos: The caravan's journey, in photos Police in riot gear block the highway to stop a caravan of thousands of Central American migrants from advancing through Mexico on Saturday. Hide Caption 4 of 60 Photos: The caravan's journey, in photos Migrants travel on a cattle truck, as a thousands-strong caravan of Central American migrants slowly makes its way toward the US border, between Pijijiapan and Arriaga, Mexico, on Friday, October 26. Hide Caption 5 of 60 Photos: The caravan's journey, in photos Migrants heading in caravan to the United States rest on the train tracks in Arriaga, Mexico. Hide Caption 6 of 60 Photos: The caravan's journey, in photos A truck of migrants heads in a caravan to the United States. Defense Secretary James Mattis is expected to sign deployment orders that could send 800 or more US troops to the border. Hide Caption 7 of 60 Photos: The caravan's journey, in photos Jensi, a 14 year old migrant girl from Honduras, baths in a fresh water stream as she and others, part of caravan of thousands from Central America en route to the United States, take rest in Pijijiapan, Mexico on October 25. Hide Caption 8 of 60 Photos: The caravan's journey, in photos Central American migrants rest for the night in Pijijiapan, Mexico, on Thursday, October 25. Hide Caption 9 of 60 Photos: The caravan's journey, in photos Families rest on a roadside between Mapastepec and Huixtla, Mexico, while traveling with thousands of migrants from Central America in a caravan en route to the United States, on Wednesday, October 24. Hide Caption 10 of 60 Photos: The caravan's journey, in photos Migrants ride on the back of a truck heading to the US border from the outskirts of Tapachula, Mexico, on Monday, October 22. The majority of migrants made their way on foot. But some also flagged down cars and trucks passing by and piled onto any vehicle that would take them. Hide Caption 11 of 60 Photos: The caravan's journey, in photos Migrants take shelter from the weather under a tarp as they rest in the town of Huixtla, Mexico, on October 22. Hide Caption 12 of 60 Photos: The caravan's journey, in photos Migrants select clothes that have been placed along the road by Mexican citizens. Hide Caption 13 of 60 Photos: The caravan's journey, in photos Migrants rest in the town of Huixtla, Mexico. Hide Caption 14 of 60 Photos: The caravan's journey, in photos Migrant men bathe using water from a fire hydrant at the main plaza in Tapachula, Mexico. Hide Caption 15 of 60 Photos: The caravan's journey, in photos A migrant caravan headed to the United States walks into Mexico after crossing the Guatemalan border on Sunday, October 21. Hide Caption 16 of 60 Photos: The caravan's journey, in photos Central American migrants hitchhike along the highway near the border with Guatemala, as they continue their journey trying to reach the United States. Hide Caption 17 of 60 Photos: The caravan's journey, in photos A Mexican Federal Police helicopter flies over migrants heading in a caravan to the United States, on the road linking Ciudad Hidalgo and Tapachula in Mexico. Hide Caption 18 of 60 Photos: The caravan's journey, in photos Central American migrants walk north toward Tapachula after departing Ciudad Hidalgo, Mexico. Hide Caption 19 of 60 Photos: The caravan's journey, in photos Local residents cheer as a migrant caravan walks into the interior of Mexico after crossing the Guatemalan border. Hide Caption 20 of 60 Photos: The caravan's journey, in photos Migrants still on the Guatemalan side of the border sleep at a temporary immigrant shelter on Sunday in Ciudad Tecun Uman, Guatemala. The caravan of thousands of Central Americans made its way into Mexico with some members hoping to eventually reach the United States. Hide Caption 21 of 60 Photos: The caravan's journey, in photos Honduran migrants, part of a caravan heading toward the United States, travel on the road linking Ciudad Hidalgo and Tapachula, Chiapas state, Mexico, on Sunday. Hide Caption 22 of 60 Photos: The caravan's journey, in photos Central American migrants walking to the United States continue their journey, departing Ciudad Hidalgo, Mexico, on Sunday. Hide Caption 23 of 60 Photos: The caravan's journey, in photos A Honduran migrant boy, part of a caravan heading to the United States, walks on the road linking Ciudad Hidalgo and Tapachula, Chiapas state, Mexico, on Sunday. Hide Caption 24 of 60 Photos: The caravan's journey, in photos Honduran migrants who have already reached Mexican soil cheer at the rest of the group still waiting to cross at the Guatemala-Mexico border bridge in Ciudad Hidalgo, Mexico, on Saturday, October 20. Hide Caption 25 of 60 Photos: The caravan's journey, in photos Children of migrants, part of the caravan, on Saturday wait with their parents to apply for asylum in Mexico at a checkpoint in Ciudad Hidalgo, Mexico. Hide Caption 26 of 60 Photos: The caravan's journey, in photos A Honduran migrant mother and her son walk on the bridge after crossing the border between Guatemala and Mexico on Saturday. Hide Caption 27 of 60 Photos: The caravan's journey, in photos Mexican paramedics help a Honduran woman who fainted after crossing the border between Guatemala and Mexico on Saturday. Hide Caption 28 of 60 Photos: The caravan's journey, in photos Honduran migrants help some of their members get down to the Suchiate River from the Guatemala-Mexico border bridge in Ciudad Hidalgo on Saturday. Hide Caption 29 of 60 Photos: The caravan's journey, in photos A migrant is comforted by a Mexican paramedic after her mother fainted while crossing the border between Guatemala and Mexico. Hide Caption 30 of 60 Photos: The caravan's journey, in photos Honduran migrants from the caravan on Saturday cross the Suchiate River, a natural border between Guatemala and Mexico. Hide Caption 31 of 60 Photos: The caravan's journey, in photos A Honduran migrant looks through the gate on the bridge that connects Mexico and Guatemala in Tecun Uman, Guatemala, on Saturday. Hide Caption 32 of 60 Photos: The caravan's journey, in photos Migrants in the caravan wait on Saturday for the opening of the gate on the bridge that connects Guatemala to Mexico. Hide Caption 33 of 60 Photos: The caravan's journey, in photos Thousands of Honduran migrants rush across the border toward Mexico, in Tecun Uman, Guatemala, Friday, October 19. Hide Caption 34 of 60 Photos: The caravan's journey, in photos A Honduran man protects his child after fellow migrants, part of a caravan trying to reach the United States, stormed a border checkpoint in Guatemala, in Ciudad Hidalgo, Mexico, Friday, October 19. Hide Caption 35 of 60 Photos: The caravan's journey, in photos Honduran migrants, part of a caravan trying to reach the United States, storm a border checkpoint to cross into Mexico, in Tecun Uman, Guatemala, Friday, October 19. Hide Caption 36 of 60 Photos: The caravan's journey, in photos Mexican federal police officers allow women and children taking part in a caravan of Honduran migrants heading to the United States to cross to Mexico in the border city of Tecun Uman, Guatemala, on Friday, October 19. Hide Caption 37 of 60 Photos: The caravan's journey, in photos An aerial view shows a Honduran migrant caravan heading to the United States as it is stopped at a border barrier on the Guatemala-Mexico international bridge in Ciudad Hidalgo, Mexico, on Friday, October 19. Hide Caption 38 of 60 Photos: The caravan's journey, in photos Honduran migrants heading in a caravan to the United States remove a barrier at the Guatemala-Mexico border bridge in Ciudad Hidalgo, Mexico, on Friday, October 19. Hide Caption 39 of 60 Photos: The caravan's journey, in photos A child is lifted over the border fence as thousands of Honduran migrants rush across the border toward Mexico, in Tecun Uman, Guatemala, Friday, October 19. Hide Caption 40 of 60 Photos: The caravan's journey, in photos A Honduran migrant mother and child are surrounded by Mexican Federal Police in riot gear, at the border crossing in Ciudad Hidalgo, Mexico, Friday, October 19. Hide Caption 41 of 60 Photos: The caravan's journey, in photos A Honduran migrant, part of a caravan trying to reach the United States, storms the checkpoint between Guatemala and Mexico in Tecun Uman, Guatemala, Friday, October 19. Hide Caption 42 of 60 Photos: The caravan's journey, in photos Honduran migrants heading in a caravan to the United States rush through the Guatemala-Mexico border bridge after tearing down its gate in Ciudad Hidalgo, Mexico, on Friday, October 19. Hide Caption 43 of 60 Photos: The caravan's journey, in photos Honduran migrants heading in a caravan to the United States crowd the gate of the Guatemala-Mexico border bridge in Ciudad Hidalgo, Mexico, on Friday, October 19. Hide Caption 44 of 60 Photos: The caravan's journey, in photos Honduran migrants wait at the Mexican border in Tecun Uman, Guatemala, on Friday, October 19. Thousands of migrants traveling in a caravan briefly moved toward the border crossing between the two countries before turning around. Guatemala has closed its border gate and is standing guard with dozens of troops and two armored jeeps. Hide Caption 45 of 60 Photos: The caravan's journey, in photos Honduran migrants leave Guatemala City, Guatemala, at sunrise on Thursday, October 18, 2018, as they make their way north toward the United States. Many of the more than 2,000 Hondurans in a migrant caravan trying to wend its way to the United States left spontaneously with little more than the clothes on their backs and what they could quickly throw into backpacks. Hide Caption 46 of 60 Photos: The caravan's journey, in photos Migrants display the flag of Honduras while on a caravan of migrants en route to the Mexican border on Thursday in Guatemala City. The caravan of thousands of Central Americans, most from Honduras, hopes to eventually reach the United States. President Donald Trump has threatened to cancel the recent trade deal with Mexico and withhold aid to Central American countries if the caravan isn't stopped before reaching the United States. Hide Caption 47 of 60 Photos: The caravan's journey, in photos A Honduran migrant, part of a caravan trying to reach the United States, pushes a stroller with a boy during a new leg of their travel in Guatemala City on Thursday. Hide Caption 48 of 60 Photos: The caravan's journey, in photos Honduran migrants in the caravan are pictured inside a truck on Thursday. Hide Caption 49 of 60 Photos: The caravan's journey, in photos Honduran migrants hike in the forest after crossing the Lempa River, on the border between Honduras and Guatemala, to join the caravan on Thursday. Hide Caption 50 of 60 Photos: The caravan's journey, in photos Honduran migrants climb into the bed of a truck in Zacapa, Guatemala, on Wednesday, October 17, 2018. Hide Caption 51 of 60 Photos: The caravan's journey, in photos A Honduran migrant, part of the caravan, rests on a street as he looks through his mobile phone in Guatemala City on Wednesday. Hide Caption 52 of 60 Photos: The caravan's journey, in photos A child lies on the ground to rest as Honduran migrants take part in a caravan to the United States in Teculutan, Guatemala, on Wednesday. Hide Caption 53 of 60 Photos: The caravan's journey, in photos Honduran migrants heading to the United States rest at a gymnasium of a Catholic church in Chiquimula, Guatemala, on Tuesday, October 16, 2018. The caravan set out October 13 from the impoverished, violence-plagued country. Hide Caption 54 of 60 Photos: The caravan's journey, in photos Honduran migrants pray at an improvised shelter in Chiquimula, Guatemala, on Tuesday. Hide Caption 55 of 60 Photos: The caravan's journey, in photos Families in the caravan rest for the night in a community gym on Tuesday in Chiquimula, Guatemala. The caravan is the second of its size in 2018. Hide Caption 56 of 60 Photos: The caravan's journey, in photos Honduran migrants move north on Tuesday near Quezaltepeque, Guatemala. Hide Caption 57 of 60 Photos: The caravan's journey, in photos Honduran migrants holds up their national ID cards as Guatemalan police block them and their caravan after the group crossed the Honduras-Guatemala border in Esquipulas, Guatemala, on Monday, October 15, 2018. Police stopped the migrants for several hours but the travelers refused to return to the border and were eventually allowed to pass. Hide Caption 58 of 60 Photos: The caravan's journey, in photos The caravan moves north after crossing the border from Honduras into Guatemala on Monday. Hide Caption 59 of 60 Photos: The caravan's journey, in photos The caravan pauses at a Guatemalan police checkpoint after crossing the border from Honduras on Monday. Hide Caption 60 of 60

They plan to cross Mexico's border in the coming days, then continue north to the United States.

Already some migrants from the caravan have begun to arrive, seeking refuge, Mexico's foreign ministry said in a statement Thursday night . And growing numbers of migrants have reached the Guatemalan city of Tecun Uman, across the winding Suchiate River from Mexico.

Comienzan a reunirse cientos de migrantes hondureños en la plaza de Tecún Uman, San Marcos. En este momento ellos tratan de decidir de qué manera cruzarán hacia #Mexico. La frontera está muy cerca de este lugar. pic.twitter.com/f0vo5vW7Ci — Michelle Mendoza (@mmendoza_GT) October 19, 2018

A bridge over the river marks an official crossing point.

Migrants have been known to cross the river on rafts for years -- sometimes encountering authorities along the way, sometimes meeting little resistance as they slipped into Mexico and continued their journey north.

This file photo from August 9, 2018, shows an area where people cross the Suchiate River from Guatemala into Mexico. The illegal crossing point is located just under the international bridge connecting the two countries, circumventing immigration and customs checkpoints.

Mexico outlines its plan

In recent days Mexican authorities have made a point of showing they were stepping up security near the country's southern border. Mexican Federal Police released a video of officers arriving in the border state of Chiapas, some toting riot gear.

Mexico's government also released a statement outlining how it planned to respond:

• Anyone with a valid visa will be able to enter and move freely.

• Anyone who wants to be recognized as a refugee or as a beneficiary of "complementary protection measures" must do so individually. Those who do so will be held "at a migratory station" for up to 45 business days.

• Anyone who enters "in an irregular manner" will be "rescued and subject to an administrative procedure and, where appropriate, will be returned to their country of origin in a safe and orderly manner."

Mexican authorities have also said they're asking for help from the United Nations High Commissioner for Refugees to process migrants seeking refugee status at the country's southern border.

This appears to be a shift from previous policies, in which humanitarian or transit visas were issued, and migrants were given the option of continuing their journey north if they didn't want to seek asylum in Mexico.

This past spring, when another caravan of Central American migrants crossed into Mexico, such policies allowed the group to make it to the US border.

JUST WATCHED This pregnant mom is the first migrant in line for asylum Replay More Videos ... MUST WATCH This pregnant mom is the first migrant in line for asylum 03:36

An 'almost impossible' situation

But there are still many unanswered questions about how this will actually play out once large numbers of migrants arrive. A complicated mix of pressures are weighing on Mexican officials as they decide how to handle the matter.

"It's a very difficult situation for the Mexican government," says Ana Maria Salazar, a former Pentagon official who's now a security analyst in Mexico City.

"It's a situation that is almost impossible to resolve at this time for Mexico," Salazar told CNN en Español Thursday.

Among the factors at play:

1) President Trump

Trump zeroed in on Mexico's role Thursday, tweeting that he cared more about the caravan than the recently renegotiated North American trade deal between Mexico and Canada. And he threatened to send troops to "shut down" the southern US border if Mexico failed to stop what he called an "onslaught."

....In addition to stopping all payments to these countries, which seem to have almost no control over their population, I must, in the strongest of terms, ask Mexico to stop this onslaught - and if unable to do so I will call up the U.S. Military and CLOSE OUR SOUTHERN BORDER!.. — Donald J. Trump (@realDonaldTrump) October 18, 2018

If Trump pulls out of the trade deal or closes the border, there would be major economic implications for both countries. If Mexico ultimately cracks down on the caravan, it would be seen as a coup for the administration in the United States -- especially among Trump's supporters -- and would speak to how successful efforts to build bridges with the Mexican government have been, even as Trump continues to boast about building a border wall.

But in Mexico, where protesters already have been marching in support of the approaching Honduran migrants, caving to US pressure wouldn't play nearly as well.

2) Migration on both sides of the border

It's important to remember that for Mexico, migration isn't just about people coming into the country, Salazar says.

It's also about Mexican emigrants living abroad, many of whom are undocumented.

"One way or another, the way Mexico treats the undocumented immigrants from Central America affects Mexico's position in how it can criticize the US government for its treatment of undocumented Mexican immigrants in the United States," Salazar told CNN en Español.

3) A presidential handoff

Mexican President Enrique Peña Nieto has partnered with the United States in the past on immigration-related issues. In recent years, Mexico has deported more Central American immigrants than the United States

But Peña Nieto is a lame duck, with less than two months left in office. So that makes any international policy negotiations tricky.

His successor, Andres Manuel Lopez Obrador, takes office December 1. During a presidential debate, Lopez Obrador indicated his administration would stop doing "dirty work" for the United States by detaining Central American migrants. He said Wednesday that his administration would offer work visas to Central Americans.

"Whoever wants to work in our country is going to have support, is going to have a work visa," he said. "We are not going to attend to the issue only with deportations or means of force."

with Peña Nieto and Foreign Minister Luis Videgaray, as well as Lopez Obrador's designated foreign minister, Marcelo Ebrard. Pompeo is scheduled to meet Fridaywith Peña Nieto and Foreign Minister Luis Videgaray, as well as Lopez Obrador's designated foreign minister, Marcelo Ebrard.

"We're looking for concrete results," the State Department said before Pompeo's trip, "and for solutions that work for both countries."