A report in the Seymour Chronicle said Chief Justice John Roberts was the only judge who appeared to be convinced by Apple's arguments which were made on Monday, seeking to shut down the anti-trust suit.
Users have brought the lawsuit to force Apple to reduce the 30% commission it charges developers who sell their apps exclusively through the App Store.
If the case succeeds, the damages paid to consumers could be tripled but first a decision has to be made on whether the case is allowed to proceed.
Apple is arguing that it has no direct connection with consumers and is merely a conduit between the app developers and those who purchase the apps.
The plaintiffs' lawyer, David Frederick, said Apple's monopoly was unique, adding that there was not a single ecommerce player who did what the company did.
A decision in whether the case can go ahead is expected early next year.