Wednesday's arguments were the third time the Coronavirus judges heard oral arguments by phone.
The telephone connection was slippery when Ginsburg began to question her, and her voice sounded weaker than normal at times. But she later came forward in the argument where she asked questions that were sometimes more like comments.
The case concerns Affordable Care Act's claim that employer-provided health insurance plans cover birth control as a preventive service and provide supporters of the Obamacare provision with those who say it violates their religious and moral beliefs.
Liberal justice repeatedly pressed the notion that women would lose coverage even if they did not share the employer's religious beliefs.
"This leaves women to hunt for other government programs that can cover them," she told Attorney General Noel Francisco, who argued for the Trump administration. "And for those not covered by Medicaid or any of the other government programs, they can get contraceptive coverage just by paying out of their own pockets, which is exactly what Congress didn't want to happen."
"You have just thrown to the wind what Congress thought was essential, that is, women get these services without any problems, at no cost to them," she added later. "Instead, you shift the employer's religious beliefs, the cost of it, to those employees who do not share those religious beliefs."
"And we believe that it also includes discretion to require most employers to give it, but not the small number who have sincere, conscientious objections," he added.
The court said Tuesday that Ginsburg expects to stay in the hospital for a "day or two."
CNN's Casey Riddle contributed to this report.