The migrant influx has taken a bipartisan political turn lately, with the Democratic mayors of New York and Washington voicing concerns about their ability to accommodate thousands of people who entered the US from its southwest border before heading north.

On Tuesday, New York City Mayor Eric Adams called on the federal government to help pay for asylum seekers headed to the nation's largest city, warning that resources are quickly being exhausted by busloads of people flocking in — emphasizing the city's "right to shelter" mandate that guarantees beds for homeless asylum seekers.

"Currently, New York City is experiencing a marked increase in the number of asylum seekers who are arriving from Latin America and other regions," Adams said in a statement. "In some instances, families are arriving on buses sent by the Texas and Arizona governments, while in other cases, it appears that individuals are being sent by the federal government."

Adams said that more than 2,800 migrants seeking asylum have entered the city's shelter system in recent weeks, and he called on Democratic US President Joe Biden to send "additional resources immediately" to help the city, saying there is "both a rapidly growing shelter population and new clients who are seeking asylum".

Washington DC Mayor Muriel Bowser went on national television this past weekend to say the homeless shelters in the nation's capital were being filled by buses sent by the states of Texas and Arizona.

While Republican governors Greg Abbott of Texas and Doug Ducey of Arizona have denied sending migrants to New York City, both have admitted to pointing buses to DC to bring what they've called a border crisis to Biden's doorstep.

Abbott began sending people in April, while Ducey started in May. Since April, Texas and Arizona have sent at least 4,000 migrants in roughly 100 buses to the nation's capital.

On Sunday, Bowser told CBS' Face the Nation that the influx of people in DC "is a very significant issue".

"We have for sure called on the federal government to work across state lines to prevent people from really being tricked into getting on buses," she said. "I fear that they're being tricked into nationwide bus trips when their final destinations are places all over the United States of America."

Renae Eze, a spokesperson for Abbott, told Fox News on Monday, "Border communities are overrun and overwhelmed, and Governor Abbott launched the border bus mission back in April to help provide support to these communities pleading for help where the Biden administration is dumping migrants.

"With our nation's capital now experiencing a fraction of the disaster created by President Biden's reckless open-border policies that our state faces every single day, maybe he'll finally do his job and secure the border."

White House press secretary Karine Jean-Pierre said during a briefing Tuesday that the administration had been in touch with Adams and Bowser and would look into their requests.

"Good luck to them on getting any help from the federal government because we've been asking for over a year and we haven't gotten much of that," Democratic Mayor Pro Tem Yolanda Ramon of Eagle Pass, Texas, told Fox News on Wednesday. The city sits on the Rio Grande, across from Mexico.

Jorge Parada, 35, told the New York Post that he, his wife and their four children left Caracas, Venezuela, and crossed into San Antonio, Texas, on July 2.

Parada said he has friends who earlier made it to New York City and decided he wanted to go there, too.

When asked why, he said, "Adventuring. It seems like a place we'd like to live. It reminds us of home. It's a metropolis."

Parada said his friends told him about staying at the intake center, so after his family met with immigration officials in San Antonio, he bought bus tickets to New York City. Upon arriving, they went to the intake center, where they were given housing in the Bronx.

Parada told the Post that he was hoping to qualify for two years of "assisted living" but was told Tuesday "that we did not qualify".

US Homeland Security Secretary Alejandro Mayorkas, speaking at the Aspen Security Forum on Tuesday, said, "Look, the border is secure. We are working to make the border more secure. That has been a historic challenge."

Brandon Judd, president of the National Border Patrol Council, said that thousands of migrants are evading border agents every day.

A total of 1,746,119 migrant encounters have been recorded in fiscal year 2022 — which started in October — as of June, according to US Customs and Border Patrol.

"As bad as the apprehension numbers are, and they are beyond bad, the scariest part of border security is the ‘gotaways' and the amount of drugs that are coming into the country," Judd told Fox News Digital, adding that the US has "the least secure border in our history".

On Wednesday, two men were indicted in connection to operating a tractor trailer rig with inside temperatures over 100 degrees F with 53 dead or dying migrants in San Antonio, officials said.

A federal grand jury in San Antonio indicted Homero Zamorano Jr, 46, and Christian Martinez, 28, both of Pasadena, Texas, in the June 27 tragedy on counts of transporting and conspiring to transport migrants illegally resulting in death; and transporting and conspiring to transport migrants illegally resulting in serious injury.