Miami (CNN) The perilous conditions migrants coming to the US face captured renewed attention from Democrats running for president on Wednesday, hours before 10 candidates take the stage for the party's first debate in Miami.

The publication of the tragic image of a drowned Salvadoran man and his young daughter , face down in the Rio Grande, after they attempted to enter the United States, led to condemnations from candidates of President Donald Trump's policies that have made it more difficult for those fleeing violence in Central America to seek asylum at ports of entry.

The candidates also rushed to visit a detention center in Homestead , where unaccompanied migrant children are being held.

Campaigns expected the first Democratic debate to include some focus on immigration, given the event will be held in South Florida. But the shocking imagery and visits to Homestead have turned the campaign's spotlight to immigration, an issue that animated Trump's campaign and united Democrats in a chorus of condemnation of the administration's policies.

The wave of trips to the detention facility was kicked off by Elizabeth Warren, who -- during a town hall in South Florida on Tuesday -- announced she would visit the detention facility hours before her debate and invited her supporters to come along.

"I'm going to Homestead tomorrow," she said. "Come with me."

Warren arrived outside the desolate, hot facility before noon on Wednesday, joined by a few dozen supporters who the campaign bussed to the facility after the senator publicly invited people to join her.

Standing atop a ladder in the 90-degree heat, a hat and sunglass clad Warren waved to children inside the facility who could be seen from the senator's vantage point as they were moved around inside the facility.

"Stop the cruelty," protesters chanted as Warren visited, free the children."

Warren is here and up on a ladder across the street from Homestead — she is waving to children inside that she can see above the wall pic.twitter.com/LOdR52cFJK — MJ Lee (@mj_lee) June 26, 2019

While some candidates had long planned to visit the detention facility during their trip to Miami for the debates, Warren's announcement seemingly set off a wave of announced visits.

Sen. Amy Klobuchar announced she would visit the detention facility Wednesday afternoon, hours ahead of when she takes the debate stage in Miami.

Jane Sanders, wife of Vermont Sen. Bernie Sanders, also visited the facility on Wednesday, telling reporters that one of her husband's first executive actions as president would be to shut down facilities like the one in Homestead.

Aides to former Housing and Urban Development Secretary Julian Castro, New York Sen. Kirsten Gillibrand, South Bend, Indiana Mayor Pete Buttigieg and California Sen. Kamala Harris all said they would visit the facility on Friday.

Former Rep. Beto O'Rourke was the first candidate to announce he planned to visit the Homestead detention facility. He plans to go Thursday, after he debates Wednesday night.

The number of visits to Homestead had put pressure on campaigns to fit the 40 miles drive from downtown Miami into their schedules, almost making visiting the detention facility a requirement in the Democratic primary.

The facility is an influx facility run by the Department of Health and Human Services for unaccompanied children, who remain there until placed with sponsors in the US. There are around 2,300 children currently at Homestead, according to Evelyn Stauffer, spokeswoman for the HHS' Administration for Children and Families.

There have been a stream of reports -- including from CNN -- of subpar conditions for children and families in the care of Customs and Border Protection, an agency within the Department of Homeland Security.

Melissa Taveras, spokeswoman for Florida Immigrant Coalition, said these visits matter, in part, because it shines a spotlight on what is happening at the facility.

"The fact that the candidates are here, it really -- even if they don't end up winning -- it allows us to take the opportunity to voice our concerns on a national platform, so that the country sees what's happening and really become sympathetic to these issues," Taveras told CNN. "Because when you think of immigrants and you think of refugees, I think people just think of them as very far away, as distant, almost inhuman. This is a really strong reality."

None of the candidates who visited or plan to visit will get into the facility. Evelyn Stauffer, spokeswoman for the HHS' Administration for Children and Families, said in a statement to CNN that while they welcome the candidates to Homestead, they "require a minimum two-week notification at the convenience and availability of the facility" to come inside.

The visits to Homestead came on the heels of a photo of the father and daughter who drowned on Sunday becoming international news. The photo, taken by Julia Le Duc, Oscar Alberto Martínez and his 23-month-old daughter, Angie Valeria, face down in murky water at the banks of the Rio Grande. The pair drowned Sunday as they were crossing from Mexico into Texas near Brownsville. They actually had made it to the Texas side initially, and Martinez placed his child there before turning around to get his wife, a journalist says. But when the daughter saw her father swimming away, she jumped in and both drowned when a strong current swept over them.

Presidential candidates responded to the photo with a mix of horror and condemnation for Trump.

"These families seeking asylum are often fleeing extreme violence," Harris tweeted in response. "And what happens when they arrive? Trump says, 'Go back to where you came from.' That is inhumane. Children are dying. This is a stain on our moral conscience."

Buttigieg told MSNBC in an interview on Wednesday morning that "there are no words" for the tragedy in the photo.

"This is the supposed to be the greatest country in the world. And the shocking thing is that part of what makes that possible is fear," Buttigieg said, adding later, "If you can look at a picture like that and say that it is acceptable to continue doing what we've been doing, then I just don't understand."

O'Rourke tweeted a blunt reaction to the image: "Trump is responsible for these deaths."

"As his administration refuses to follow our laws -- preventing refugees from presenting themselves for asylum at our ports of entry -- they cause families to cross between ports, ensuring greater suffering & death. At the expense of our humanity, not to the benefit of our safety," he said on Twitter.

Bernie Sanders called the photo "just one painful example of so many that demonstrate the reckless disregard for basic humanity that have come from Trump's policies."

And New Jersey Sen. Cory Booker tweeted that people "should not look away" from the photo.

"These are the consequences of Donald Trump's inhumane and immoral immigration policy. This is being done in our name," he added.

Immigration is one area of the Democratic primary where most of the candidates are unified, not just against Trump's policies, but on what they would do if the President is outed from the White House in 2020.

At least three candidates on the debate stage on Wednesday night -- Castro, O'Rourke and Warren -- have unveiled comprehensive immigration plans.

Castro, whose grandmother came to the United States from Mexico, unveiled an extensive immigration plan in April that looked roll back a series of laws implemented under Presidents George W. Bush and Donald Trump, including decriminalizing crossing the border illegally. Castro was the first candidate in the crowded 2020 Democratic field to unveil a detailed immigration plan.

"Absolutely heartbreaking," Castro tweeted in response to the photo. "Families are fleeing desperate conditions to find refuge, only for the doors to be shut in their face. We need a more sensible, compassionate immigration system that doesn't criminalize desperation.

Warren said this week she agrees with Castro that border crossings should be decriminalized

And O'Rourke brings a mix of personal experience and policy. The former congressman lives on a hill in El Paso overlooking the US-Mexico border and is bilingual. O'Rourke also brought attention as a Texas Senate candidate last year to the swelling population of migrant children who had been separated from their parents and were being kept at a detention facility in Tornillo.

After a town hall with the American Federation of Teachers on Tuesday, O'Rourke told reporters that "Donald Trump is the most openly racist president that we've had."

"It's that rhetoric that has led to the practices that we're seeing at Homestead; the practices that we're seeing in my hometown of El Paso, Texas," he said.