Washington (CNN) Supreme Court justices were deeply divided Tuesday over whether the Trump administration can add a citizenship question to the 2020 census , with the conservative justices showing signs that they were inclined to vote in favor of allowing the question.

After more than an hour and a half of arguments where the justices repeatedly interrupted each other and counsel, Justices Samuel Alito and Neil Gorsuch suggested that Commerce Secretary Wilbur Ross was within his right to add the question.

Chief Justice John Roberts asked questions that seemed at times favorable to the administration, and Justice Brett Kavanaugh stressed that Ross has discretion in the area and that other countries ask a similar question. He called it a "common question" internationally.

The four liberal justices pounced on the administration's argument however, asking whether the addition of the question would reduce the number of respondents to the census. Justice Stephen Breyer asked why Ross overruled census officials in making his decision.

Justice Sonia Sotomayor was perhaps the most persistent questioner. She pressed Solicitor General Noel Francisco on why the question was being asked of all recipients after some "65 odd years" of being left off. She said there was "no doubt" that people -- non citizens and their households -- would respond less. Justice Elena Kagan told Francisco that she searched the record for Ross's justification in 2018, but came up empty. She suggested that Francisco was providing a kind of "post hoc rationalization" after the decision was made.

The case comes on the eve of the 2020 census and represents the Supreme Court's foray into an issue that goes to the core of political representation. The new conservative majority on the court -- solidified with the addition of two Trump nominees -- will have to weigh in on critics' allegations that the administration is acting in a way to stunt the political influence of minorities.

The Constitution requires that every person be counted in the country each decade, and the census provides critical data that is used for issues such as the allocation of congressional seats and the distribution of billions of federal dollars to states and localities. Opponents of the question, which has not been asked of all recipients since 1950, say it will lead to a decrease in response rates by the millions.

Lower courts

Lower courts have ruled against the government, pointing to the administration's shifting rationale for reinstating the question and held that the way the government proceeded was illegal.

Ross's decision was unlawful for a "multitude of independent reasons and must be set aside," Judge Jesse M. Furman of the U.S. District Court for the Southern District of New York ruled in January in a 277-page opinion after holding an eight-day trial.

Furman said that Ross' decision to add the question violated the Administrative Procedure Act, a federal law that governs the way that agencies can propose and establish regulations. He said that Ross failed to consider several important aspects of the issue, and "alternately ignored, cherry-picked or badly misconstrued the evidence in the record before him."

Most critically, Furman said that Ross's stated rationale for the question, to promote the enforcement of the Voting Rights Act, was "pretextual -- in other words, that he announced his decision in a manner that concealed its true basis rather than explaining it," as the Administrative Procedure Act required him to do, the judge held.

It was back in March of 2018 that Ross announced that the Department of Justice -- then still led by former Attorney General Jeff Sessions -- had requested that the Census Bureau reinstate the question in order to obtain "more effective enforcement" of the Voting Rights Act.

Ross acknowledged that adding the question "could reduce" response rates, but said that more accurate citizenship date would outweigh such fears.

"After a thorough review of the legal, program and policy considerations, as well as numerous conversations with the Census Bureau leadership and interested stakeholders," Ross wrote, he had decided to proceed.

But after a trial, Furman said that Ross' justification in a March 2018 letter that announced the reinstatement was "materially inaccurate."

Furman -- drawing from documents and testimony -- wrote that Ross, almost as soon as he arrived in office in February of 2017, began asking questions about adding a citizenship question. He spoke about the issue with Sessions, as well as immigration hardliners such as then political adviser Steve Bannon and Kansas Secretary of State Kris Kobach. Those consultations, as well as the new timeline, undermined the stated justification for the question, Furman held.

The judge also pointed to the fact that the Census Bureau believed that there were other ways to obtain more accurate measures of citizenship.

In testimony, Dr. John Abowd, the Census Bureau's chief scientist, was asked whether he was under the impression that his work on the question mattered.

"Yes," he said.

Abowd was then asked if he had ever been told that Commerce had in fact initiated the process to insert the question. "No one told me that," Abowd testified. Furman noted that the doctor "choked up" and visibly held back tears.

Constitutional questions at play

Although Furman didn't rule on the Constitutional questions, a judge sitting on the US District Court for the District of Maryland held that Ross' action violated the Enumeration Clause of the Constitution, which provides for an "actual enumeration" every decade.

"Because the Secretary ignored evidence regarding the impact of the question and provided no legitimate rationale to support it, the addition of the citizenship question would unreasonably compromise the distributive accuracy of the Census and the addition violates the Enumeration Clause," Judge George J. Hazel of the US District Court for the District of Maryland held in April.

Francisco stressed in court briefs that the citizenship question was legal and that "nothing in the record supports the district court's extraordinary charge that the secretary of commerce" lied about his rationale for the decision.

Francisco accused the court of straining "to read every statement and action of the secretary in the worst possible light."

As a threshold argument, Francisco argued that the challengers in the case -- 18 states, cities, and non-profit groups, among others -- do not have the legal right or "standing" to bring the case.

In order to come to court, they would have to prove an injury, and Francisco argued they can't base that injury on a third party's "speculative" refusal to answer the question.

"None of respondents' alleged injuries will materialize if individuals completely and truthfully answer the census questionnaire, as required by federal law," he said.

Francisco argued that if the justices allow the plaintiffs to bring the case it would "permit any demographic question on the census to be challenged so long as a group of individuals disproportionately residing in certain states announce their intent to illegally boycott" the question.

He also said that Ross' action is not reviewable under the Administrative Procedure Act because "courts do not have the authority to second guess the secretary's decision" in part because the Constitution vests Congress with "virtually unlimited discretion" in conducting the census. Congress, he said, delegated the authority to the secretary of commerce.

But even if the action was reviewable, Francisco argued "it simply cannot be 'arbitrary'" or "irrational" to reinstate to the decennial census a question whose pedigree dates back nearly 200 years.

Francisco's position drew the support of 16 states, all Republican-led which wrote Ross asking him to adopt the question.

Democratic-led states are leading the opposition

But 18 other states, cities and non-profit groups disagree.

They say that the Constitution and the Census Act require the federal government to count every person in the country, every 10 years, and that Furman held that adding the citizenship question would reduce responses among households with a non-citizens totaling roughly 6.5 million.

"There is just one chance, each decade to get the enumeration right," New York's Attorney General Letitia James told the justices in court papers.

She outlined the injury to states including the possibility of losing a seat in the House of Representatives and the loss of funds from federal programs.

James said that not only did Ross violate the Administrative Procedure Act but also the Constitution's Enumeration Clause that requires and "actual" enumeration of the population every 10 years. She said that adding the question would "affirmatively undermine the accuracy of the enumeration."

Another set of challengers represented by the ACLU argued that since 1950 the government realized that a "differential undercount" of racial and ethnic minorities would threaten census accuracy.

"The government stopped asking this question, along with dozens of others on the census when it realized that these questions were harming the accuracy of the population count and were specifically causing an undercount of communities of color," Ho said.

Lawyers for the Democratic-led House of Representatives will also have the opportunity to argue before the Supreme Court justices on Tuesday against the addition of the question.

In addition, five former directors of the Census Bureau, who have served under both Democratic and Republican administrations, filed a friend of the court brief supporting the challengers. They argued that they have a "unique expertise" of processes and procedures required to conduct an "accurate, high-quality" census.

"The longstanding view of the Census Bureau -- reaffirmed by several recent Census Bureau analyses -- is that addition of the question will reduce the accuracy of the population," their lawyer told the justices.