Washington (CNN) The number of families crossing illegally from Mexico into Texas and Arizona has continued to spike in October, according to federal officials in both states, as President Donald Trump keeps raising his rhetoric on immigration and a caravan of thousands of migrants is traveling through southern Mexico.

The increase is causing difficulty at every stage for the Department of Homeland Security, including at the border processing facilities, for Immigration and Customs Enforcement detention and at shelters for unaccompanied minors, as well as at Greyhound stations in South Texas, where many migrants are released and travel around the US, said a senior DHS official, who asked to have their name withheld because they were not authorized to speak publicly.

All the facilities from processing to detention are "breaking at the seams," said the official.

This comes as Trump has railed against the caravan ahead of the midterm elections, calling its participants "criminals" and threatening to cut off aid to Central American countries that don't stop the progress north. The administration has accused migrants of abusing the US asylum system and has faced increased political pressure from the President to stop the flow of illegal immigration.

Homeland Security Secretary Kirstjen Nielsen, in an interview Thursday on Fox News, said "everything is on the table," including cutting off aid to foreign countries, to stop "lawless groups of people heading towards the border."

"Every measure we have tried, every measure we haven't tried, everything is on the table to make it very clear that we have a sovereign right to protect our citizens," she said.

Nielsen, who was in Yuma, Arizona, on Thursday, told local officials that DHS is working with Mexico daily to address the caravan issue and ensure that those seeking asylum are offered it in Mexico, according to Yuma Mayor Douglas J. Nicholls, who attended the meeting.

"Our sector has a large percentage of family units that have been coming through from Central America," said Nicholls.

Preparing for caravan, migrants

Customs and Border Protection in Texas is planning for the potential arrival of the caravan by meeting with stakeholders, in case it comes that way, said the DHS official. The official likened it to planning for a hurricane, because you have to monitor the direction of the caravan and plan as needed.

DHS is tracking two caravans, one massive one with thousands of migrants and another, smaller one that formed in El Salvador.

But the more pressing issue may be the migrants already at the border.

"We are having a difficult time managing the high numbers we have right now," said the DHS official about the surge in the Rio Grande Valley.

The number of family members apprehended in the Rio Grande Valley, the most active sector of the southern border, is expected Friday to exceed such apprehensions for September, according to the official, who was familiar with the latest numbers.

The most recent official border apprehension numbers released by Customs and Border Protection earlier this week were for September, which showed a record high month with 16,658 family apprehensions across the southern border.

The Yuma sector had a record high in September with 2,187 family apprehensions, according to available data going back to 2013.

While the Rio Grande Valley had a high for the fiscal year in September, with 8,782 family member apprehensions, there were over 10,000 family members apprehended in both November and December of 2017.

The soon-to-be record in Texas indicates there could be another big month of family crossings across the southern border.

October, the first month in the fiscal year, is "seeing numbers that far surpass last fiscal year" in the region, said the official on Thursday.

In order to deal with the influx and to mitigate the risk of holding family units past the time frame allotted to the government, ICE began curtailing all reviews of post-release plans from families apprehended along the Southwest border on Tuesday, according to ICE spokesperson Sarah Rodriguez.

This means ICE will be releasing recently apprehended families without reviewing their travel and communication plans. The possible consequences could be an increased burden on nongovernmental organizations receiving the families or having families released into local communities or bus stations without pre-coordinated travel plans.

This practice, which was ended in Arizona earlier this month, has now been terminated all along the southern border.

However, Teresa Cavendish, director of operations at Catholic Community Services of Southern Arizona, which works with recent migrants released from custody, said she was skeptical that ICE had previously been doing extensive pre-coordinated travel, based on their experiences with migrants.

Her organization, which has assisted in coordinating temporary lodging and services for hundreds of families in Arizona this month, said the message from ICE was "don't stand down," in anticipation that the caravan could arrive in their state, she said.

"There continues to be uncertainty and nobody quite knows what we will be called upon to do if the migrant caravan arrives," she said.

"After decades of inaction by Congress, the government remains severely constrained in its ability to detain and promptly remove families with no legal basis to remain in the U.S. As a result, family units continue to cross the border at high volumes and are likely to continue to do so, as they face no consequence for their actions," said Rodriguez in a statement to CNN.

There are no signs that the number of families attempting to cross illegally is slowing down.

At the end of fiscal year 2018, families and unaccompanied minors accounted for about 51 percent of the apprehensions in the Rio Grande Valley, compared with about 64 percent so far in October, the DHS official said.

Families entering the US illegally "have really, really skyrocketed," said the official on Thursday.

The total number of apprehensions in October in the Rio Grande Valley, which accounts for 40 percent of all illegal crossings, is also expected to surpass September, according to the official.

Wednesday, there were 870 US Border Patrol apprehensions in the sector. Apprehensions are used by Border Patrol as a measure of illegal crossings.

The number of families illegally crossing also increased in October from September in the Yuma sector of Arizona, where hundreds of families have been released from immigration custody in recent weeks, according to Vincent Dulesky, special operations supervisor for the Border Patrol's Yuma sector.

In Yuma, the spike forced ICE to set up temporary processing at the Border Patrol facilities last week to speed it up, said Dulesky. Migrants who cross illegally are processed by Border Patrol and turned over to ICE for further immigration proceedings, such as expedited removal or release pending a court date.

Dulesky said that in Yuma, families are climbing the border fence and in many cases sustaining injuries, which requires additional manpower from Border Patrol. The surge in Arizona has "become a huge strain" on the resources of the NGOs and religious community, which helps recently released migrants transition to destinations throughout the US.

"It's kind of like an unfunded humanitarian crisis," said Dulesky.