Washington (CNN) In selecting judges for top US courts, President Donald Trump has searched for reliable conservatives who would reduce federal regulatory power over the environment and energy, worker safety and consumer affairs.

As then-White House counsel Don McGahn told an audience a year after Trump took office, "There's a coherent plan here, where actually the judicial selection and the deregulatory effort are really the flip side of the same coin."

That plan will be tested in a fresh case on Tuesday over the constitutionality of the Consumer Financial Protection Bureau, a brainchild of Elizabeth Warren , now a US senator and Democratic presidential contender.

CFBP was created in 2010 during the fallout of the 2008 financial crisis to safeguard consumers in banking, mortgage, credit card and other financial transactions.

But there is more at stake than the future of one agency. The new case set for oral arguments on Tuesday provokes core questions of how involved government should be in people's lives and how far presidential power should extend.

A court ruling on the President's removal power could affect a multitude of independent agencies including the Federal Trade Commission, Federal Energy Regulatory Commission and Federal Reserve Board. For more than a century, Congress has been creating such agencies within the executive branch with directors who can only be removed only "for cause." The CFPB director, for example, holds a five-year term and cannot be removed by the President except for "inefficiency, neglect of duty, or malfeasance in office."

The question for the justices is whether that limit on the President's power breaches the constitutional separation of powers. The Trump Justice Department says the CFPB setup is unconstitutional. It is siding with a California debt-services firm, Seila Law, whose practices had triggered a CFPB probe. While both the Justice Department and Seila Law say the President should have more control over CFBP, they differ on the fate of the full agency. (Seila Law says it should be struck down; the administration would preserve it, but with more presidential control.)

Ultimately, the case could affect the regulatory power of "roughly a third of the modern federal government," according to lawyer Paul Clement, whom the high court appointed to defend the CFPB when the Trump administration chose not to.

Larger themes

By their past writings, justices in the Roberts Court majority have demonstrated that they share the Trump anti-regulation emphasis.

The court has increasingly taken up disputes over what Justice Neil Gorsuch, Trump's first Supreme Court appointee, has called "the explosive growth of the administrative state over the last half-century."

Federal agencies touch every part of daily life, Gorsuch observed in one case last year, "with reams of regulations" to which "agencies add thousands more pages of regulations every year."

But, as more liberal justices have pointed out, those regulations can clarify laws regarding protections for people with disabilities, transportation security, mine safety and additional public concerns. The current case involves an agency created after the 2008 financial catastrophe that burst the housing bubble, shrunk retirement accounts and diminished household wealth. It laid bare a multitude of predatory lending practices and underwritten credit.

The Trump administration, and the more conservative justices, assert broad and concentrated authority in the presidency and shun limitations on his power to hire or fire executive branch officials.

When now-Justice Brett Kavanaugh wrote an opinion as a lower court judge against the CFPB in a separate dispute, he declared the CFBP "unconstitutionally structured."

"This is a case about executive power and individual liberty," he wrote in a 2016 opinion that was later reversed by the full US Court of Appeals for the DC Circuit. "The U.S. Government's executive power to enforce federal law against private citizens -- for example, to bring criminal prosecutions and civil enforcement actions -- is essential to societal order and progress, but simultaneously a grave threat to individual liberty."

To safeguard that liberty, Kavanaugh wrote, the Constitution lodges full responsibility for executive power with the President, who is elected and accountable to the people.

The philosophical and practical stakes of this case have prompted dozens of outside interests to weigh in.

"What a strange time in our history for the court to be poised to eliminate key constraints on presidential power," wrote Deepak Gupta, a former senior counsel at the CFPB, in a recent SCOTUSblog post . Gupta, now in private appellate practice, also filed a "friend of the court" brief on behalf of financial regulation scholars backing the CFPB.

Among the outside groups siding with the Trump administration and Seila Law, the California firm engaged in debt services, is the Chamber of Commerce. Lawyer Andrew Pincus, representing the Chamber, argued in a "friend of the court" brief that when Congress tried to shield the bureau from political influence, it eliminated political accountability.

Noting that the bureau has wide-ranging enforcement power, including the ability to levy civil penalties of up to $1 million a day, Pincus asserted that a structure "born from a dream of creating an apolitical, European-style technocracy that would set consumer finance policy" has become "an American nightmare."

How the challenge reached the Supreme Court

Congress created the Consumer Financial Protection Bureau as part of the Dodd-Frank Wall Street Reform and Consumer Protection Act (named for its congressional sponsors). Lawmakers wanted a streamlined agency to protect consumer interests in mortgages, credit and other consumer financial services.

Warren, at the time a Harvard law professor, and others had initially proposed a multi-member board to oversee the bureau, but Congress ultimately decided on a single director. President Barack Obama appointed the first CFPB director, Richard Cordray

The current director, named by Trump, is Kathleen Kraninger. She has subscribed to the Trump stance that she could be removed by the President at will.

The case of Seila Law v. CFPB began after the bureau began seeking documents and other information from Seila Law to determine whether it was violating the federal Telemarketing Sales Rule by illegally charging consumers upfront fees for debt-relief services.

In fighting the CFPB enforcement action, Seila Law challenged the board's structure. Its lawyer, Kannon Shanmugam, tells the justices that because that the director setup is unconstitutional, the entire agency is invalid.

"In creating the CFPB... Congress tied its very existence to its freedom from the President," he said in his written brief, adding that "Congress affirmatively sought to prevent the President from exercising control over the CFPB."

The Trump administration does not go that far, saying, "there is no basis to conclude that Congress would have preferred to have no Bureau at all rather than a Bureau headed by a Director" who the President could remove at will.

But like Seila Law, the administration takes a strong ideological stand against independent agencies. Shanmugam and US Solicitor General Noel Francisco focus their arguments on the CFPB single-director structure, but both say the high court would have grounds to overrule a 1935 precedent that barred the President from easily removing the five Federal Trade Commissioners.

Most independent agencies are directed by multi-member boards.

Paul Clement back in court

Traditionally the Justice Department defends government agencies. When the administration opts against it, as happened in this case, the Supreme Court appoints a lawyer to file a brief and argue for the government entity.

The choice of outside lawyer is usually made by the justice who oversees emergency motions and other matters from the regional circuit that heard the case. Justice Elena Kagan, a liberal who oversees the California-based 9th Circuit, recommended Clement, a former US solicitor general in the Republican George W. Bush administration who has unassailable conservative credentials.

That may blunt the momentum against the CFPB and other independent agencies. Clement enjoys respect by both sides of the bench and last week was publicly congratulated by Chief Justice John Roberts for making his 100th argument before the court.

In his legal filing, Clement contends the dispute is not ripe for a decision because Trump has not tried to remove the director, and if he tried, the current director has said she would leave willingly.

"This case involves an effort by the CFPB to enforce a garden-variety civil investigative demand," Clement wrote, arguing that the enforcement action had a tenuous connection to the director's removal status. "[S]ubsequent events have severed the connection entirely," he adds, noting that since the action against Seila Law was first filed by Cordray, a Trump appointee who believes she can be readily removed has taken over.

If the court were to reach the constitutional merits, Clement adds, the Constitution allows Congress to "impose modest restrictions on the President's removal authority."

"No one can deny that Congress has been imposing such restrictions on agencies for nearly a century and a half, and doing so with the unanimous endorsement of this Court for 85 years," Clement argues. "To change course now and call into question much of the structure of the federal government would be an overruling without precedent in the history of precedent."