(CNN) — The Supreme Court on Tuesday questioned the Biden administration's authority to prioritize which non-citizens to deport when hearing a challenge brought by two Republican state attorneys general who say the Department of Homeland Security is skirting federal immigration law.

The justices were considering three distinct issues in the case, which opens the door to shifting majorities. After arguments, it wasn't clear if there was a clear majority in any one area.

The case, brought by Texas and Louisiana, is the latest salvo from conservative states who have all but declared war on the Biden administration on immigration and have gone as far as busing undocumented immigrants to Democratic-led states in an effort to raise alarm about the issue.

At the heart of the dispute is a September 2021 memo from Homeland Security Secretary Alejandro Mayorkas that laid out priorities for the arrest, detention and deportation of certain non-citizens, reversing efforts by former President Donald Trump to increase deportations.

Several of the conservative justices on Tuesday seemed ready to rule in favor of the states on a major threshold issue: whether Texas and Louisiana had the legal right to bring the challenge in the first place.

Justice Samuel Alito seemed strongly in support of the states, arguing they could show the necessary legal harm to get into court. At one point, Alito told a lawyer for the Biden administration that her argument against the states' standing showed a "special hostility" to the states.

Liberal Justice Elena Kagan, however, strenuously responded that immigration policy is the "zenith" of federal power and if the two states were to prevail in this case, "every" immigration policy going forward is going to be challenged. She said a combination of the states and sympathetic courts could bring immigration policy to a "dead halt."

Turning to the merits of the case -- whether the Biden administration's guidelines conflicted with two provisions of federal law -- Alito, Chief Justice John Roberts and Justice Brett Kavanaugh repeatedly pointed out that the law says that some immigrants "shall" be taken into custody or removed suggesting some skepticism about the administration's discretion in the area.

"Shall means shall," Roberts said. "Shouldn't we just say what the law is," he suggested, and leave it to the other branches to figure out how to comply with it. But later, both Roberts and Kavanaugh acknowledged a key argument put forward by the government: that Congress had not provided the necessary funds for the government to try to remove every non-citizen.

Roberts told a lawyer for the two states that it was "impossible for the executive to do what you want it to do." Kavanaugh picked up on that point, noting that the government has argued "we don't have the money to comply." He noted that the resources "aren't there."

"If you prevail," he asked the states' lawyer, "what will happen?"

In court papers, Solicitor General Elizabeth Prelogar stressed that Congress has never provided the funds to detain everyone, prompting administrations to consider how to prioritize limited funds.

"Especially given perennial constraints on detention capacity, the Executive retains authority to focus its limited resources on those non-citizens who are higher priorities for apprehension," she wrote.

The guidelines call for an assessment of the "totality of the facts and circumstances" instead of the development of a bright-line rule. The government lists aggravating factors weighing in favor of an enforcement action including the gravity of the offense and the use of a firearm, but it also lists mitigating factors that include the age of the immigrant.

Lawyers for Texas and Louisiana argued that the government lacked the authority to issue the memo because it conflicts with federal law. They point to immigration law that holds that some immigrants "shall" be taken into custody or removed.

"When Congress required the Executive to act, the Executive lacks the authority to disregard that instruction," Texas Attorney General Ken Paxton argued in court papers. He also charged that the guidelines violate the Administrative Procedure Act, a federal law that governs how an agency can issue regulations.

A district court judge blocked the guidelines nationwide. "Using the words 'discretion' and 'prioritization' the Executive Branch claims the authority to suspend statutory mandates," ruled Judge Drew Tipton, a Trump appointee on the US District Court for the Southern District of Texas. "The law does not sanction this approach."

A federal appeals court declined to issue a stay of the decision, prompting the Biden administration to ask the Supreme Court for emergency relief last July. A 5-4 court ruled against the administration, allowing the lower court's decision to remain in effect while the legal challenge plays out.

Conservative Justice Amy Coney Barrett joined her three liberal colleagues in dissent without providing any explanation for her vote.

In his memo, Mayorkas stated that there are approximately 11 million undocumented or otherwise removable non-citizens in the country and that the United States does not have the ability to apprehend and seek to remove all of them. As such, the Department of Homeland Security sought to prioritize those that pose a threat to national security, public safety and border security.

Prelogar noted that the lower court holding against the government "runs counter to longstanding practice spanning multiple administrations" and emphasized that the guidelines are not binding orders compelling action, but instead, are an attempt to utilize available resources while leaving ultimate discretion to the judgment of individual immigration officials.

"The guidelines simply tell federal officials how to enforce federal law in a field that the Constitution commits to the federal government," Prelogar wrote.

As a threshold matter, she urged the justices to dismiss the challenge, arguing that the states don't have the legal right -- or standing -- to bring the challenge because they can't show the necessary direct injury. Prelogar said if the lawsuit were allowed to go forward, any state could sue the federal government about "virtually any policy."

In a separate dispute, Arizona, Montana and Ohio also sued the Biden administration. A district court judge issued a nationwide injunction blocking the guidelines, but the 6th US Circuit Court of Appeals put that decision on hold.

"Federal law gives the National Government considerable authority over immigration policy," the court held. It also expressed skepticism about whether the guidance directly injured the states.

Paxton argued to the Supreme Court that the states have the legal right to bring the lawsuit because they bear costs related to law enforcement activities as well as health care and education costs of the non-citizens.

Critics also say that Texas is guilty of "judge shopping" the case at hand by filing it where it had a 100% chance of drawing a Trump-appointed district judge who has previously issued nationwide injunctions concerning other immigration policies.

"So far, Texas has taken the lead in 29 different lawsuits against the Biden administration, on immigration," said CNN analyst Steve Vladeck who is a professor at the University of Texas School of Law. In a friend of the court brief filed opposing Texas, Vladeck noted that none of those cases had been filed where the Texas government is located in Austin.

"This case is the latest battlefield in what has become an all-out war by red state attorneys general against virtually every Biden related policy," Vladeck said.

This story has been updated with additional details.

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