Aside from offering members the opportunity to seek asylum in Mexico, local authorities have done little to impede the progress of the Honduran migrant caravan that has continued its journey to the US southern border, aided by foreign aide groups like Pueblo Sin Fronteras and others. And as several thousand have already turned back thanks to the rampant crime and other grueling aspects of the journey, the pervasive atmosphere of lawlessness nearly cost one member of the caravan his life after he was badly beaten this weekend by a gang of vigilantes who had accused him of "child stealing."

Blaming the tensions associated with the searing heat and little access to food, a local police chief described to the Associated Press how the man was viciously beaten after a dispute in a food line spiraled out of control.

Raul Medina Melendez, security chief for the tiny municipality of Tapanatepec in Oaxaca state said the town was distributing sandwiches and water to migrants camped in the central square Saturday night. When a man with a megaphone asked people to wait their turn, some men hurled insults at him. "Finally people got really angry and those below began to attack the guy," Medina said. As the man ran, a false rumor spread that he had grabbed a child for protection and he was caught and beaten. Police rescued him and took him to a hospital for treatment, though his condition wasn’t immediately clear.

On Sunday, several members of the caravan denounced the attack, as the man lay wounded in a nearby hospital, his condition unclear.

"Is that the way we’re going to always behave?" a woman from Honduras asked. "Anytime there’s a rumor everyone is going to run to beat up someone?" Others complained of a few smoking marijuana or complained that images of litter and uneaten food made them appear disrespectful. On Saturday, an arm of the federal government for the first time seemed to be directly helping the migrants advance rather than trying to diminish the caravan. Grupo Beta, Mexico’s migrant protection agency, gave rides to stragglers and passed out water. "There are people fainting, there are wounded," said Martin Rojas, an agent of Grupo Beta who spoke to The Associated Press after dropping off a group of women and children in Tapanatepec after spotting them on a highway trudging through temperatures approaching 104 degrees Fahrenheit (40 degrees Celsius).

Meanwhile, in a last-ditch attempt to try and convince the Central Americans to stay in Mexico, outgoing Mexican President Enrique Pena Nieto announced what amounted to a program of government handouts, dubbed "you are home" which promised the migrants shelter and medical attention and schooling if they agreed to stay in southern Mexico, according to ABC.

But the migrants weren't having it. Apparently, the risk of making it into the US in the face of Trump's threats and a troop surge at the border still seems more appealing than accepting their lot in Mexico. The rest of the 4,000 or so migrants refused the offer, though Mexico's Interior Ministry did issue permits to 111 of the migrants, which would allow them to stay and work in Mexico. Mot of those who accepted the permits were pregnant women, children and the elderly.

As the Washington Examiner reported, a large block of migrants voted to reject Mexico's offer.

"Thank you!" they yelled as they voted to reject the offer in a show of hands in the town of Arriaga. They then added: "No, we're heading north!" Sitting at the edge of the edge of the town square, 58-year-old Oscar Sosa of San Pedro Sula, Honduras concurred. "Our goal is not to remain in Mexico," Sosa said. "Our goal is to make it to the (U.S). We want passage, that's all."

Afterward, Mexico tried a more heavy handed approach, sending 100 federal officers to block a stretch of highway. But they eventually left after a human rights group intervened.

Earlier Saturday, more than 100 federal police dressed in riot gear blocked a highway before dawn to encourage the migrants to apply for refugee status in Mexico rather than continuing the journey north. Police let the caravan proceed after representatives from Mexico’s National Human Rights Commission convinced them that a rural stretch of highway without shade, toilets or water was no place for migrants to entertain an offer of asylum. Many members of the caravan have been travelling for more than two weeks, since a group first formed in San Pedro Sula, Honduras.

The migrants are still 1,000 miles away from the closest border crossing at McAllen Texas. However, the trip could be twice as long the Tijuana-San Diego frontier, as another caravan did earlier this year. Only about 200 in that group made it to the border.

And as their numbers have already dwindled from more than 10,000 to around 4,000, it's likely that more will turn back - and accept another Mexican offer of safe passage home - as they reckon with the fact that it would take another 100 days to reach the nearest border crossing, given that the migrants, who often must walk with small children, are moving at a pace of roughly 10 miles per day, as CNN reported.

At this rate, instead of reaching the border by election day, as the media has speculated, the caravan wouldn't arrive until Feb. 1. Maybe, by then, Mexico's offer of asylum in its southern states will have started to look somewhat more appealing...

..which means that, the only way for the caravan to become an issue in the midterm elections would be for the groups aiding them to pile them on to trucks and speed them to the border.