Eagle Pass, Texas (CNN) — As the migrant crisis continues at the US-Mexico border and beyond, tensions between Texas and federal officials remain high.

Cold, hungry and bloodied from razor wire grazes.

This was the reality for one Venezuelan couple as they spent two days waiting to turn themselves into immigration authorities on the US side of the Rio Grande, which is lined by sharp razor wire and shipping container border barriers.

Kevin, 25, and Vanessa, 21, left their home in Venezuela for Mexico three weeks ago, fleeing a regime they’ve protested against for years, they told CNN Wednesday.

Now they’ve found themselves in the middle of the ongoing border battle between Texas and the US federal government.

CNN is sharing the couples’ first names only for safety reasons.

With only the clothes on their backs and a belt bag across their bodies, the architecture students, who spoke to CNN through thick layers of razor wire, said they only had one viable option: to cross the river through high water levels and strong currents, losing most of their belongings throughout the journey.

Home was no longer in Venezuela, a place where the pair said they have no rights. And home couldn’t be Mexico either, because of how dangerous it is, they said.

Their end goal, having endured the difficult conditions of the journey to the US, was to seek asylum once they arrived.

“We are dying of thirst and cold,” Kevin said.

Vanessa and Kevin hadn’t eaten since their wait for authorities began and were only able to share a single bottle of water between them, which a soldier with the Texas National Guard handed to them earlier in the day Wednesday, they said.

Under federal policy, migrants like Kevin and Vanessa would have surrendered two days ago, been taken into custody by federal authorities and transported for immigration processing.

But in Eagle Pass, the zone recently taken over by Texas, migrants who jump the fence or crawl between the razor wire are arrested and charged with criminal trespassing, according to the Texas Department of Public Safety.

The razor wire lining the border is so dense, you can hardly see through it. What is visible are pieces of fabric, presumably clothing, caught in the middle of wired loop after loop stretching across the 2.5-mile line of fencing.

Despite the Supreme Court’s ruling this week allowing federal Border Patrol agents to remove the wire while the state’s legal challenge to its removal plays out, it still remains intact.

The concertina wire was installed by Texas authorities in the Eagle Pass area – recently the epicentre of the migrant crisis and near where three migrants drowned this month.

The federal government doesn’t have an immediate plan for a mass removal unless the situation changes drastically or there is an emergency, a law enforcement source familiar with operations told CNN.

However, given the high court’s ruling Monday, federal law enforcement can and will cut or remove the wire as needed to enforce immigration laws and in the case of medical emergencies, the same source said.

Federal agents were standing ready to breach the fencing to render aid to any individual in distress or if otherwise deemed “operationally necessary,” another enforcement source told CNN Tuesday.

The only way to get to the other side is up and over one of the shipping containers that run parallel to the barbed wire fence – and that’s exactly what Kevin and Vanessa did several hours after speaking with CNN, helping each other jump down onto the Shelby Park area.

Moments later, Texas National Guard members were seen contacting Texas DPS officers who then arrived and took them into custody, a CNN team observed.

The takeover at Shelby Park by Texas authorities is a separate dispute from the razor wire legal battle that is also expected to play out in the courts, the same source added.