Supreme Court justices across the ideological spectrum seemed inclined Monday to find President Obama lacked the constitutional authority to make high-level government appointments at a time he said the Senate was not available to provide its advice and consent.

The Constitution provides the president the ability to make such appointments when the Senate is in recess. But when Obama made appointments to the National Labor Relations Board in January 2012, the Senate was holding pro forma sessions every three days precisely to thwart the president’s ability to exercise the power.

“It really is the Senate’s job to determine whether they’re in recess or whether they’re not,” said Justice Elena Kagan, who was nominated by Obama and who directed her remarks during Monday’s oral arguments at Donald B. Verrilli Jr., her successor as Obama’s solicitor general.

But Kagan also appeared to be advocating the narrowest way to resolve what Justice Stephen G. Breyer called “political fights between Congress and the president.”

She and other members of the court seemed to agree with Senate Republicans and others who challenged Obama’s action that the text of the recess clause — that the president “shall have power to fill up all vacancies that may happen during the recess of the Senate” — might favor the narrow reading an appeals court gave it.

But they also acknowledged that the power has been used thousands of times by nearly every president since George Washington to make appointments to the highest levels of the military and executive and judicial branches.

Kagan said she worried that 200 years of practice would be upended if “we would wake up one fine morning and chuck all of that because all of a sudden we happened to read the clause” differently.

Verrilli agreed, telling Chief Justice John G. Roberts Jr. that “a stable equilibrium . . . emerged over the course of this country’s history between the two branches. After all, what we are advocating for here is the status quo.”

The case is a rarity in that the Supreme Court has never had reason to play referee on the issue before and has no precedent to rely on. While the current battle is between Obama and Senate Republicans, the tension has existed equally when a Republican has occupied the White House and Democrats objected to his appointments.

There was more riding on the outcome before Senate Democrats late last year changed the filibuster rules to make it easier for the president’s nominees to be confirmed on a majority vote. But the conflict would be in play whenever one party controlled the executive branch and the other ruled the Senate.

The packed courtroom underscored the importance of the fight — White House press secretary Jay Carney sat on the same bench as Senate Republican Leader Mitch McConnell (Ky.) And there was plenty of firsthand experience with the appointments process.

Both Roberts and Kagan saw their first attempts to join the judiciary fail when the Senate declined to vote on their appeals court nominations. Miguel Estrada, who represented McConnell, was filibustered when President George W. Bush nominated him to the bench.

And Justice Antonin Scalia’s son, Eugene, was a recess appointment by Bush as solicitor of the Labor Department.

The court faced three questions:

● Does the phrase “the recess of the Congress” mean that the president can make such appointments only during the once-a-year breaks between sessions of Congress — which could last days or only moments — or whenever the Senate took an extended break?

● Does the phrase “vacancies that may happen during the recess” mean the president may fill only vacancies that arise during that period, as the challengers contend, or vacancies that exist during that time? The first reading would drastically reduce the number of jobs the president could fill.

●May the president make recess appointments when the Senate convenes only every three days in pro forma sessions in which it says it will conduct no business?

It is the last question that prompted the case. Senate Democrats started the pro forma sessions in 2007 to stop Bush’s attempt to make recess appointments. Despite encouragement from his advisers to challenge the legitimacy of the sessions, he declined.

But when Obama became president and the membership of the NLRB fell to two members because Senate Republicans blocked votes on the president’s three nominees, Obama took action. Despite the pro forma sessions, Obama took note of the Senate’s declaration that no business would be conducted, and made his nominees recess appointees.

A bottling company in Washington state that lost an NLRB ruling challenged the legitimacy of the members, and the panel of the D.C. appeals court went beyond the question of pro forma sessions to severely restrict the president’s power.

Scalia asked Verrilli what he should do if he agreed with the appeals court reading of the recess appointments clause even though the practice of presidents and Congresses has gone the other way.

Verrilli resisted the question as long as he could before finally saying the court should defer to the practice.

“So if you ignore the Constitution often enough, its meaning changes?” Scalia asked.

Kagan wondered whether the recess appointment power, born of Colonial times when Congress took long recesses and travel was difficult, was a “historical relic.”

And Roberts picked up on that theme. The problem for presidents is not that the Senate is unavailable to approve nominees but that it won’t.

“You’re latching on to the Recess Appointment Clause as a way to combat that intransigence rather than to deal with the happenstance that the Senate is not in session when a vacancy becomes open,” Roberts told Verrilli.

Washington attorney Noel J. Francisco, representing the company challenging the appointments, said the Senate’s advice and consent power was an important constitutional check on the president, and the government was seeking to make it meaningless.

But some justices thought his argument had the same flaw.

“Your argument would destroy the recess clause,” said Justice Ruth Bader Ginsburg. “Under your argument, it is totally — totally within the hands of the Senate to abolish any and all recess appointments.”

The case is NLRB v. Noel Canning.