* Justices hear case on first day of new 9-month term
* Case involves the legal rights of 25 million workers (Adds quotes from Justices Bryer, Ginsburg and Kennedy, details from argument)
By Lawrence Hurley and Robert Iafolla
WASHINGTON, Oct 2 (Reuters) - Liberal U.S. Supreme Court justices on Monday defended the right of workers to bring class-action claims against companies but their conservative counterparts who are in the majority sounded skeptical in the biggest business case of the court's new term.
A win for employers would give the green-light to an already growing trend in which companies require workers to sign arbitration agreements waiving their right to bring class-action claims either in court or before private arbitrators.
About 25 million workers are already bound by such agreements, according to the left-leaning Economic Policy Institute think tank.
The nine justices heard roughly an hour of arguments in the case on the first day of their new nine-month term. They also heard arguments in an immigration dispute, and have a series of major cases lined up in the coming months regarding voting rights, religious liberty, union funding and other issues.
Liberal Justice Stephen Breyer said he was worried that a ruling against the workers would imperil "the entire heart of the New Deal," laws and programs enacted in the 1930s under President Franklin Roosevelt to help workers during the Great Depression.
"I haven't seen a way that you can, in fact, win the case, which you certainly want to do, without undermining and changing radically what has gone back to the New Deal," Breyer told Paul Clement, a lawyer representing the employers.
Employers have increasingly required employees to sign waivers to guard against a rising tide of worker lawsuits seeking unpaid wages. Class-action litigation can result in large damages awards by juries and is harder for businesses to fight than cases brought by individual plaintiffs.
Liberal Justice Ruth Bader Ginsburg said the ability of workers to join together to bring claims against an employer was the "driving force" behind a key federal law enacted to regulate labor disputes.
Many cases involve claims that, if brought on their own, would represent such a minor dollar amount that they may not be worth pursuing because of legal bills alone, Ginsburg added.
"That's why this is truly a situation where there is strength in numbers," Ginsburg said.
The court has a 5-4 conservative majority but two of the five conservative justices were silent: Republican President Donald Trump's appointee to the court, Neil Gorsuch, and Clarence Thomas, who typically does not speak during oral arguments.
Justice Anthony Kennedy, often the swing vote in major cases, asked questions that signaled sympathy to employers, as did two fellow conservatives, Chief Justice John Roberts and Justice Samuel Alito.
Kennedy indicated that a loss for workers would not prevent them from acting in concert because they would still be able to join together to hire the same lawyer to bring claims, even though the claims would be arbitrated individually. That would provide "many of the advantages" of collective action, Kennedy said.
If the workers win, "it seems to me quite rational for many employers to say, 'Forget it, we don't want arbitration at all,'" Kennedy said.
The three consolidated cases that came before the justices involved professional services firm Ernst & Young LLP, gas station operator Murphy Oil USA Inc and healthcare software company Epic Systems Corporation.
The Trump administration sided with companies, contending that the agreements are valid. In a rare occurrence, the administration faced off against an independent agency of the federal government, the National Labor Relations Board (NLRB).
The Justice Department in June reversed the government's previous position taken in the case under Democratic former President Barack Obama, deciding not to defend the NLRB's stance that these employment agreements were invalid.
None of the justices addressed the flip-flop on Monday.
Justice Department lawyer Jeffrey Wall said the NLRB made a "pretty radical move" five years ago when it claimed a worker's legally protected right to act together to improve the workplace included the right to class-action lawsuits.
Federal labor law does not stretch so far that it prevents a court from enforcing an agreement to bring claims against employers in individual arbitration, Wall added.
"You can be protected from dismissal for retaliation when you seek class treatment up to the courthouse doors or the doors of an arbitral forum, but once you're inside, you don't have an entitlement to proceed as a class," Wall said.
The NLRB argues that the waivers violate federal labor law and let companies evade their responsibilities under workplace statutes. Workers have fought back against the waivers, arguing that the cost of pursuing their cases individually in arbitration is prohibitively expensive.
A ruling is expected by the end of June.
Reporting by Lawrence Hurley and Robert Iafolla; Editing by Will Dunham