The White House on Monday insisted most of the thousands of unaccompanied minors flooding across the border will be deported.

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The firm position came as President Obama was set to travel to Texas, the center of a growing firestorm over the nation’s inability to prevent illegal immigrants from entering the country.

Obama is set to hold fundraisers in Dallas and Austin during the two-day trip, but he has no plans to visit the border, where officials have struggled for months to contain a wave of minors seeking refuge in the United States.

The president has come under criticism from members of both parties over the wave of immigrants, who have filled detention centers and overwhelmed a court system ill-prepared to handle the surge.

Rep. Raúl Grijalva (D-Ariz.), the co-chairman of the Congressional Progressive Caucus, on Monday said “the borderlands deserve a presidential visit.”

“I think a visit by the president is reaffirming that the borderlands along the Southwest border are vital and important to this nation,” Grijalva said during an interview with MSNBC. “So I think it would be important and very symbolic.”

The White House is expected to ask Congress this week for $2 billion in supplemental funding to help deal with the crisis. Some of the money will be used to bring in additional immigration lawyers, judges and asylum officials in the hope that trials can be sped up to deport more of the children sooner.

As Obama’s trip approached, the White House insisted Monday it was “not worried” about the optics of the president raising cash with Texan donors without going to see the developing crisis firsthand, even as Texas Gov. Rick Perry Rick PerryOVERNIGHT ENERGY: Democrats push resolution to battle climate change, sluggish economy and racial injustice | Senators reach compromise on greenhouse gas amendment stalling energy bill | Trump courts Florida voters with offshore drilling moratorium OVERNIGHT ENERGY: Trump signs major conservation bill into law | Senate votes to confirm Energy's No. 2 official | Trump Jr. expresses opposition to Pebble Mine project Senate votes to confirm Energy's No. 2 official MORE (R) pressured Obama to go to the border.

“The president is very aware of the situation that exists on the southwest border,” White House press secretary Josh Earnest said Monday.

Obama has the difficult task of arguing that he does not “have to be there in order to see the problem and deal with it effectively,” said Southern Methodist University political scientist Cal Jillson.

“They have to work the optics as best they can because going to the border with Gov. Perry would provide him an opportunity to grandstand, which he would almost certainly do,” Jillson said.

Growing concern within the West Wing about the political and policy problems surrounding the immigrant children seems evident.

Earnest offered the hardest line yet on the estimated 52,000 children who have crossed the border this year, vowing “most” would be returned to their native countries.

“Based on what we know about these cases, it is unlikely that most of these kids will qualify for humanitarian relief,” Earnest said. “And what that means is, it means that they will not have a legal basis for remaining in this country and will be returned.”

There are no simple political or policy solutions to a crisis in which unaccompanied minors as young as four years old are reportedly crossing the border for sanctuary.

The young people, primarily from Guatemala, El Salvador and Honduras, are said to be fleeing violence in their home countries, though the administration has acknowledged many believe they will be able to stay in the United States.

The administration has argued that’s not the case, but the sheer number of young people crossing the border has stretched resources thin.

All minors automatically get a chance to apply for asylum in the United States.

Applicants must prove either that they are a victim of human trafficking or deserving of political asylum — meaning the chances they’ll be allowed to stay are slim. In most cases, applicants would need to prove they are part of a targeted class that is suffering persecution at the hands of the government and that their home government is unable or unwilling to protect them.

As those cases work through the judicial process, immigrant children are often given to U.S. relatives for care, reinforcing the perception that children crossing the border will be allowed to stay.

There’s also no guarantee people will show up for their day in court.

Leaving the immigration issue untouched in Texas would open up the administration to fresh attacks that the president isn’t doing enough to address the flood of immigrant children.

“The next time the president wants to lecture Republicans on immigration, he should instead reflect on his habit of politicizing the humanitarian and border crisis occurring on the U.S.-Mexico border while prioritizing money and politics when he has a chance to do his job,” Republican National Committee spokeswoman Izzy Santa said Monday.

But going to the border would create a spectacle, and one that could reverberate badly for Democrats in November.

Rep. Eddie Bernice Johnson (D-Texas) said Monday she didn’t see any reason for the president to visit the border.

The president is similarly handcuffed in how the administration could handle the influx of minors within the confines of existing law.

The administration is wary of asking Congress to change the law granting asylum, saying hastened action could have rippling consequences and put children at greater risk.

“There are some important benefits to this law,” Earnest said Monday, noting that the legislation offered crucial protections to children from Asia who are the victims of human trafficking.

And human rights groups have denounced proposals to address the crisis by allowing Border Patrol agents to make immediate determinations about whether children should be eligible for asylum proceedings.

The crisis and limited avenues for responding are taking a political toll on the White House, experts say.

Democrats had hoped to make immigration reform a central issue of the midterm campaigns, contrasting Republican inaction in the House with the Senate’s bipartisan reform bill.

But the crisis “complicates the claims that the border is under control and presenting less of a problem,” Jillson said.

“The crisis has given Republicans political ammunition which may well weaken him further, and stirs the Republican base, which is still very much for increased security measures and against any type of pathway to citizenship,” he said.

Updated at 8:31 p.m.