Washington (CNN) Chief Justice John Roberts has tried to offer ballast in today's political turmoil, asserting the independence of the judiciary and rebuking President Donald Trump's suggestion that Republican justices will automatically rule for him, and Democratic ones will do the opposite.

Now the Supreme Court faces a high-profile test of a major Trump agenda item and the question is how Roberts' declaration of independence, along with his new role at the ideological center of the court, might affect the tone of Tuesday's oral arguments and an ultimate decision affecting the 2020 census.

In dispute is whether Census forms will, at the direction of Commerce Secretary Wilbur Ross, include a citizenship question . Census Bureau officials have predicted the inquiry would lead to a lower response rate and an undercount of Hispanic and non-citizen households. The result could be a loss of federal funding and political power for mainly Democratic states and cities.

As in last year's controversy over the Muslim travel ban, the census dispute centers on a Trump policy that lower court judges not only declared invalid but the product of suspicious justification.

Last year, Roberts in the end took the lead to uphold the travel ban affecting majority-Muslim countries. The court looked past Trump statements revealing animus toward Muslims and favored executive prerogatives in the national security context.

The citizenship question is more directly related to political power and Republican versus Democratic interests. As such, the stakes for the court's reputation as a neutral player and the simmering conflict of Roberts versus Trump are even higher.

The case's importance is reflected in the nearly 50 "friend of the court" briefs filed at the high court, most on the side of the challengers, including from a group of former US trial court judges who warn, perhaps with an eye to Roberts, that the integrity of the judiciary hangs in the balance.

Urging the justices to defer to US District Court Judge Jesse Furman's findings regarding duplicitous Commerce Department explanations for the citizenship question, the former judges wrote that "reaffirming the legitimacy and competence of trial courts is particularly critical today" as the judicial system is under attack.

When Furman ruled, he observed that the Constitution requires the government to count every person in the United States, irrespective of the person's citizenship status. Pointing up the consequences of a decennial census, he said, "The population count derived from that effort is used not only to apportion [US] Representatives among the states but also to draw political districts and allocate power within them. And it is used to allocate hundreds of billions of dollars in federal, state, and local funds."

In its appeal, the Trump administration argues that the Supreme Court should not even address whether the Commerce Department acted arbitrarily in adding the citizenship question as Furman had ruled. Administration lawyers say the Commerce Secretary has "virtually unlimited discretion" over the census form, largely because no manageable standards exist to evaluate the propriety of questions.

The challengers, more than a dozen Democrat-dominated states and cities led by the New York attorney general, rely on an opinion written last year by Roberts that said agency action was subject to a "strong presumption" of judicial review . The challengers also cite a 1992 opinion by now-retired Justice John Paul Stevens that said judicial review helps ensure public confidence in the census and "strengthen this mainstay of our democracy."

Roberts' new role on the court

The retirement of Justice Anthony Kennedy last year, and Trump's appointment of Justice Brett Kavanaugh to succeed him, hardened the Supreme Court's 5-4, conservative-liberal split. It also put Roberts, long to the right of Kennedy, at the ideological median point.

At the same time, the tumultuous Kavanaugh confirmation hearings last fall prompted increased public concerns about the high court's independence.

Responding to that atmosphere, Roberts shortly after Kavanaugh was confirmed in October stressed that, as justices, "we do not sit on opposite sides of an aisle, we do not caucus in separate rooms, we do not serve one party or one interest. We serve one nation."

Then in November, Roberts countered a Trump complaint that an "Obama judge" had ruled against the administration. "We do not have Obama judges or Trump judges, Bush judges or Clinton judges," Roberts said in a statement. "What we have is an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them."

Whether that ideal is a reality may be disproportionately in Roberts' hands because he is now at the crucial middle of the high court. Already this term, he has moved slightly to the left. In February, for example, he cast the fifth vote, with the four liberals, to block a strict Louisiana abortion regulation . The disputed law was similar to a Texas law invalidated by the high court in 2016, over a Roberts dissent.

Tensions on the court

From the start, the census case has splintered Supreme Court justices. In a series of orders late last year, they declined to interfere with the start of Furman's trial but blocked him from obtaining testimony from Ross about his explanations for adding the citizenship question.

When Ross announced the decision in spring 2018, he said question would help ensure enforcement of the Voting Rights Act. He said that the Justice Department had asked that the question be added, but he later acknowledged, after email evidence was revealed as part of the New York lawsuit, that he had earlier consulted with White House adviser Steve Bannon.

In November, the justices issued a brief order saying they would hear the Trump administration appeal regarding evidence Furman was using in the case. But before the justices could hold their hearing -- oral arguments were scheduled for February -- Judge Furman ruled. In a 277-page January opinion covering a multitude of evidentiary and legal issues, Furman found Ross' decision to be "arbitrary and capricious" in violation of the Administrative Procedures Act.

The Trump administration's appeal is backed by "friend of the court" filings from the Republican National Committee, several Republican-controlled states and such conservative organizations as Citizens United.

Led by the Oklahoma attorney general, the Republican state officials said Furman wrongly accepted assertions that people might decline to reveal their citizenship status out of fear of legal action. "But irrational fears cannot be the basis for holding that a census question is invalid—lest every census question beyond simple enumeration be invalidated," the Republican state officials argued, adding that "both as a practical matter and as a result of robust legal protections, answering any census question poses zero risk to census respondents."

Joining the Democrat-dominated challengers are civil rights groups, the former judges, and former Census Bureau directors, among others.

Five former Census Bureau directors who served under both Democratic and Republican administrations expressed concerns in their brief that the citizenship query, as an untested "last-minute addition," could significantly drive down participation.

More fundamentally, they insisted, "given today's cynicism about government," the census could become perceived "as a political exercise rather than an important part of our civic life."