Legal experts say the courts will have to first determine if there is proper jurisdiction to decide such a matter, then consider whether the president is overstepping his bounds. The National Emergencies Act does not define what is and is not considered an emergency, leaving presidents with wide latitude.
Meanwhile, Trump is moving ahead with plans. Two Pentagon-funded contracts for replacement wall projects in Arizona and New Mexico were announced last week totaling $976 million.
Held up as a way to deter illegal immigration, the Department of Justice in the spring of 2018 implemented a "zero tolerance" stance: cross illegally and face criminal prosecution.
The program had a shaky rollout in Southern California, a busy federal court district used to handling only serious or particularly egregious immigration violations. Soon, the average of less than two misdemeanor illegal entry cases per month skyrocketed to more than 800 per month.
A special fast-track court was set up to hear the cases, and border-crossers were allowed to plead guilty the same day with little to no jail time.
The flow was so heavy that calendars went late into the night, interpreters could not be found for many non-Spanish speakers, attorneys had difficulty finding time to meet with clients and hearings were punctuated daily with arguments of due process violations.
The process grew so contentious that four months in, the court's magistrate judges decided to take same-day pleas off the table, giving defendants now up to five days to decide how to proceed.
Trump backed off of true zero tolerance in response to growing public backlash over the policy's most controversial byproduct: family separation.
But the special illegal entry court still processes the misdemeanor cases, with more of a focus on adults traveling without children these days.
Even before zero tolerance began, the Trump administration was routinely separating families. Two mothers sued, kicking off what became the landmark litigation in San Diego that resulted in the reunification of thousands of families and a stern rebuke of how the administration disregarded the family unit.
The class-action litigation and related lawsuits, overseen by U.S. District Judge Dana Sabraw, does not outright ban family separation when parents are criminally prosecuted. But it does require families to be reunited as soon as the criminal case is over, for the duration of their administrative immigration process that follows.
Separations are also permissible when the children appear to be in danger, the parentage is in doubt or the parent is deemed unfit.
The case also forced a blueprint for tracking separated families in the future, to avoid the chaos that caused at least 400 parents to be deported and left kids in the U.S. fighting immigration cases on their own.
Trump said last week he has no plans of reinstating family separations, blaming the practice on the Obama administration -- which separated families but on a much smaller, limited scale. In the same breath, Trump went on to imply separations helped stem border crossings.
"I'll tell you something, once you don't have it that's why you have many more people coming. They are coming like it's a picnic, like 'Let's go to Disneyland.'"
With the order to keep families together during the civil immigration process, the Trump administration says it now faces a shortage of detention space to house them.
The administration has repeatedly criticized the terms of a 1997 court settlement known as the Flores agreement, which puts limits on the amount of time children can be held in immigration detention and regulates their housing conditions.
But the family separation case has bumped up against the Flores agreement, leaving the administration with a few options: detain the families together; separate the family and house the children in shelters with parental consent; or release the families in the community on parole.
Faced with the surge in arriving migrant families -- many who are claiming asylum -- the government said it has been left with no other option than to release the families on parole, sometimes with GPS monitoring.
The so-called "catch and release" practice has been widely criticized by conservatives as an incentive for families to continue to migrate north. The Trump administration says once released, the families disappear into the U.S. and wait years for their immigration cases to proceed, with few showing up for their hearings.
According to Justice Department data, removal orders were filed against 4,599 asylum-seekers in 2017 who failed to show up for court. About 119,000 asylum applications were filed that same year.
The administration tried to amend the Flores settlement in Los Angeles federal court, to lengthen the time kids could be detained, but a Los Angeles judge denied the request last July.
Courts have also found problems with the broad detention of asylum-seekers. A federal judge in Seattle earlier this month ordered bond hearings within seven days for those who pass the initial "credible fear" screenings. The U.S. must also prove why the migrants shouldn't be released.
However, in another case, the Supreme Court handed Trump a victory last month when it comes to legal immigrants who have past crimes on their records that could trigger deportation. The 5-4 vote upheld the government's ability to take such immigrants into custody and hold them indefinitely during their immigration case, even if they served their sentences long ago.
The fate of so-called Dreamers has been an early point of contention in the Trump era, one the president has tried to use as a bargaining chip with congressional Democrats when it comes to overhauling immigration laws.
The 2012 Deferred Action for Childhood Arrivals, or DACA, program, allows young people who were brought illegally to the U.S. as children to go to school or work in the U.S. as long as they register and remain law abiding.
When the attorney general announced in September 2017 that he was terminating DACA, several lawsuits followed.
So far, DACA has survived.
In one lawsuit, filed by California Attorney General Xavier Becerra, the University of California and others, a federal judge in San Francisco issued a preliminary injunction that allows current DACA participants to renew their status.
The government has twice petitioned the U.S. Supreme Court to intervene, and the high court has declined once already. In November, the 9th Circuit upheld the preliminary injunction, ruling the plaintiffs were likely to win on their claim that the termination of DACA was "arbitrary and capricious" and therefore unlawful.
In a new attempt to get it before the high court, the government has argued that the 9th Circuit ruling orders the U.S. to "preserve a policy that affirmatively sanctions the ongoing violation of federal law by 700,000 aliens who have no lawful immigration status and no right to the policy's continuation."
Other lawsuits are ongoing in New York, Texas and Washington, D.C.
In the summer of 2017, the Trump administration began requiring cities to cooperate with immigration enforcement to be eligible for federal anti-crime grants.
Many communities and states that have enacted so-called "sanctuary" policies pushed back with lawsuits, including California.
The Trump administration has argued that laws that prohibit local law enforcement from sharing the immigration status of those in their custody creates a public safety issue. In turn, some cities and states argue that residents who fear immigration enforcement are less likely to cooperate with local police, in turn making communities less safe.
So far, the courts have largely sided with the states.
In December, a Manhattan federal judge ruled in favor of New York state and city, Connecticut, New Jersey, Washington, Massachusetts and Virginia, stating the information-sharing requirement "impinges on (the states' and city's) sovereign authority and their citizens' liberty to be regulated under their preferred state and local policies."
The ruling follows similar ones in California, Illinois and Pennsylvania, although none of the orders have resulted in a nationwide injunction on the DOJ grant rules.
In reaching their decisions, some judges pointed to a 2018 Supreme Court decision, penned by conservative Justice Samuel Alito, that struck down a federal law that required states to ban sports gambling. That could temper Trump's chances at the high court.
One of the few immigration moves to make it to the Supreme Court has been Trump's executive order severely restricting travel to the U.S. from several predominately Muslim countries for national security reasons. Two lower federal appeals courts had earlier blocked it.
In June, the high court found in favor of Trump in a 5-4 vote split along ideological lines. The ruling affirmed the president's power to secure the borders, despite his anti-Muslim-tinged remarks made in conjunction with the travel ban.
"We must consider not only the statements of a particular president, but also the authority of the presidency itself," Chief Justice John Roberts wrote.
The ban affects travel from eight nations, six of them predominately Muslim: Iran, Libya, Somalia, Syria, Yemen, Chad, North Korea and Venezuela.
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