Vice President Kamala Harris acknowledged the situation.
"Joe Biden doesn't want you to see", Cruz told reporters at the Capitol.
President Joe Biden has tasked Vice President Kamala Harris with taking charge of efforts to stem the flow of migrants to the southern border, as the administration struggles to handle a surge of people - including many unaccompanied minors - flowing into USA illegally via Mexico.
By putting her in charge of addressing the growing humanitarian crisis on the US-Mexico border, Biden has given Harris a significant portfolio laced with both political opportunity and peril.
Critics have charged the shift in tone has encouraged more people to attempt the journey, with many Republicans seeking to portray the situation as a "crisis".
"It's a huge problem", the vice president told CBS News. "I'm not going to pretend it's not".
Since Biden's inauguration, the United States has seen a spike in the number of people encountered by border officials.
According to analysis from the Pew Research Center, there were nearly 19,000 family members counted in February this year, up by 168 percent from January.
"I can think of nobody who is better qualified to do this", Biden said at a White House meeting with Harris and other top officials as thousands flee violence in impoverished Central America.
One television network was granted access to pool coverage of Wednesday's tour by White House officials and lawmakers of the center in Carrizo Springs, Texas.
USA officials are battling to house and process an increasing number of unaccompanied children, many of whom have been stuck in jail-like border stations for days while they await placement in overwhelmed government-run shelters. "While we are clear that people should not come to the border now, we also understand that we will enforce the law and that we also - because we can chew gum and walk at the same time - must address the root causes that cause people to make the trek, as the President has described, to come here". However, a spokesperson for the couple subsequently said Wednesday, "Zara and Mike Tindall are happy to announce the birth of their third child, Lucas Philip Tindall".
"Should these kids be in the custody of HHS, Health and Human Services, instead of the Border Patrol?"
"Dealing with what we need to do around aid in a way that is about developing those countries so that we also deal with the cause of why people are coming into our country", she said. On the bathroom floor", he said.Asked if he was hands-on at the birth, Tindall revealed that a friend of Zara's who had been present at the birth of the couple's previous children was on hand again."She was there and recognized that we wouldn't have got to hospital in time, so yeah, it was running to the gym, get a mat, get into the bathroom, get the mat on the floor, towels down, brace, brace, brace."Tindall added, "Fortunately the midwife who was going to meet us at the hospital wasn't that far away so she drove up, and got there just as we'd assumed the position".
"There is no question that this is a challenging situation", said Ms Harris.
She added that two Biden administration envoys were now travelling to Mexico and Guatemala where the White House says they will seek "to develop an effective and humane plan of action to manage migration".