On the litigation center's website, the group highlights a quote from Carter G. Phillips, a partner at Sidley Austin who often represents the chamber in the Supreme Court.
"Except for the solicitor general representing the United States, no single entity has more influence on what cases the Supreme Court decides and how it decides them than the National Chamber Litigation Center," he said.
Phillips said in an interview that he often asks the chamber to file a brief in his cases because he believes it gets the court's attention.
"My first thought is to turn to the chamber for amicus help," he said. "They know how to present the arguments in a way that's designed to maximize the positive effect."
But legal experts said the influence of the chamber, or any other group, on the Supreme Court is exaggerated. In cases where the court has ruled in the chamber's favor, University of Pennsylvania law professor Kermit Roosevelt said, "It's more likely that they are seeing eye-to-eye."
"It's a pretty pro-business court, so those cases would probably be coming out the same way without the Chamber of Commerce participating," he said.
The justices receive briefs from advocacy groups of all stripes and perspectives, so it's not just the chamber that has a say. In the Wal-Mart case, labor unions and consumer rights advocates were among the 28 interest groups to state their arguments in the case.
The briefs are intended to inform the justices' decision, or perhaps introduce a new argument in the case. But Roosevelt said they often do not have any influence at all.
"Generally speaking, interest groups matter if they show the court a perspective that the court wasn't aware of. It's unlikely that the chamber was doing that," he said. He added that, for the justices, "The outcomes of the cases are more important to them than any lobbying group."
Lee Epstein, a University of Southern California law professor, agreed that the chamber's influence might be overstated.
But she added that effective arguments can sway court opinion. Over the years, Epstein said, it's likely that the chamber has figured out which ones those are.
"It could be that they've just gotten really good at this game," she said.
Vice President Joe Biden waits to conduct a mock swearing-in ceremony with Sen. Brian Schatz, D-Hawaii, in the Capitol's Old Senate Chamber, December 2, 2014. Schatz was sworn in to serve the remainder of his term since he was appointed to the seat after Sen. Daniel Inouye, D-Hawaii, passed away.