The court's three liberals dissented.
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Legal challenges to the law are ongoing at a federal appeals court, but the decision hands a significant - yet temporary - win to Texas, which has been battling the Biden administration over immigration policy.
The court had been blocking the law from taking effect, issuing an indefinite pause on the proceedings a day earlier, which was wiped away by Tuesday's order.
Senate Bill 4, signed into law by Republican Gov. Greg Abbott in December, makes entering Texas illegally a state crime and allows state judges to order immigrants to be deported. Immigration enforcement, generally, is a function of the federal government.
The law immediately raised concerns among immigration advocates of increased racial profiling as well as detentions and attempted deportations by state authorities in Texas, where Latinos represent 40% of the population.
A federal judge in Austin had blocked the state government from implementing the law. But the 5th US Circuit Court of Appeals granted a temporary stay of the lower court's decision and said the law would take effect on March 10 if the Supreme Court didn't act. A pair of emergency appeals from the Biden administration and others soon followed.
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Abbott on Tuesday called the court's order a "positive development" but acknowledged the case will continue in the appeals court.
As is often the case in emergency applications, the Supreme Court did not explain its reasoning.
However, a concurring opinion written by Justice Amy Coney Barrett, joined by Justice Brett Kavanaugh, explained that the appeals court had handed down only a temporary "administrative" order. Barrett appeared eager to keep the Supreme Court out of reviewing such orders.
"So far as I know, this court has never reviewed the decision of a court of appeals to enter - or not enter - an administrative stay," Barrett wrote. "I would not get into the business. When entered, an administrative stay is supposed to be a short-lived prelude to the main event: a ruling on the motion for a stay pending appeal."
Barrett said she thought it was "unwise to invite emergency litigation in this court about whether a court of appeals abused its discretion at this preliminary step."
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Justice Sonia Sotomayor, whose dissent was joined by fellow liberal Justice Ketanji Brown Jackson, said the order "invites further chaos and crisis in immigration enforcement."
The law, Sotomayor wrote in her dissent, "upends the federal-state balance of power that has existed for over a century, in which the National Government has had exclusive authority over entry and removal of noncitizens."
"Texas can now immediately enforce its own law imposing criminal liability on thousands of noncitizens and requiring their removal to Mexico," Sotomayor wrote. "This law will disrupt sensitive foreign relations, frustrate the protection of individuals fleeing persecution, hamper active federal enforcement efforts, undermine federal agencies' ability to detect and monitor imminent security threats, and deter noncitizens from reporting abuse or trafficking."
Justice Elena Kagan noted in her brief dissent that her view of the issues in the case "are, as always in this posture, preliminary."
"But the subject of immigration generally, and the entry and removal of noncitizens particularly, are matters long thought the special province of the Federal Government," the liberal justice continued.
The New Orleans-based appeals court is set to hear arguments in the case on April 3.
Case could soon return to the high court
Barrett and Kavanaugh, two critical votes on the high court, wrote that the justices should stay out of second-guessing appeals courts when it comes to very short-term "administrative" pauses that are generally used to give courts a few additional days to review the briefs.
Barrett wrote that if the 5th Circuit doesn't issue a decision soon, the Biden administration and the other parties in the case could return to the Supreme Court.
"The time may come, in this case or another, when this court is forced to conclude that an administrative stay has effectively become a stay pending appeal and review it accordingly," she wrote. "But at this juncture in this case, that conclusion would be premature."
Tami Goodlette, an attorney representing some of the law's challengers, called the court's order "unfortunate" and said it "needlessly puts people's lives at risk."
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"We remain committed to the fight to permanently overturn S.B. 4 to show the nation that no state has the power to overtake federal immigration authority," she said.
Fight over controversial law
The Biden administration, two immigration advocacy groups and El Paso County are challenging the law.
In its appeal to high court, attorneys for the administration argued the law would "profoundly" alter the status quo "that has existed between the United States and the States in the context of immigration for almost 150 years."
"People can disagree about immigration. They always have. And Texas may be deeply concerned about recent immigration," attorneys for the immigration groups and El Paso County wrote in court papers. "But the same was true of California in the 1870s, Pennsylvania and Michigan in the 1930s, and Arizona in 2012. Nevertheless, for 150 years this Court has made clear that states are not allowed to regulate the core immigration field of entry and removal."
Texas Attorney General Ken Paxton, a Republican, and other state officials had told the Supreme Court that the "Constitution recognizes that Texas has the sovereign right to defend itself from violent transnational cartels that flood the State with fentanyl, weapons, and all manner of brutality."
The officials described Texas as being "the nation's first-line defense against transnational violence" and said the state has been "forced to deal with the deadly consequences of the federal government's inability or unwillingness to protect the border."
On Tuesday, Paxton posted his excitement about the news on X, formerly known as Twitter.
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