WASHINGTON — The Obama administration faced a fresh challenge to its health care law just as many of its key provisions took effect Wednesday, after an eleventh-hour Supreme Court ruling temporarily allowed some Catholic groups not to cover birth control in their employee health plans.

The requirement that employers cover contraception and related medications and procedures has been one of the most controversial parts of the Affordable Care Act, leading to dozens of lawsuits from groups that say it violates their religious freedom. The Supreme Court will hear arguments on the issue this year.

The decision came on the eve of what administration officials described as a landmark moment, as new health insurance policies began for about 6 million Americans who were set to receive coverage under the law.

Hospitals nationwide reported a relatively quiet day, without any surge of newly insured people filling emergency rooms with pressing medical needs. The White House reported no problems.

“People are going to be surprised by how little happens” right away, said Ashish Jha, a Harvard University professor who has studied the implementation of the universal health-care law in Massachusetts. “We’re all thinking there will be this new flood of people. And there will be some people with pent-up demand, but I think there’s a lot more slack in the system than we give it credit for.”

Wednesday also marked the start of some of the law’s most popular provisions, such as one that prevents insurance companies from rejecting people who have preexisting conditions. And it was technically the first day that most Americans must have health coverage or pay a fine, although the law includes a three-month grace period.

But those developments were overshadowed by the latest twist in the controversy over the contraception mandate. The provision requires that most employers provide health plans that cover an array of medications and procedures – including the birth control pill, the morning-after pill and permanent measures such as tubal ligation – without a co-pay.

As recently as Tuesday, the head of the U.S. Conference of Catholic Bishops complained in a letter to President Barack Obama that some people have gotten reprieves from aspects of the law, but not those who oppose the mandate.

The legislation “harshly and disproportionately penalizes those seeking to offer life-affirming health coverage in accord with the teachings of their faith,” Archbishop Joseph Kurtz wrote.

Justice Sonia Sotomayor issued the stay late Tuesday. It came at the request of an order of nuns from Colorado, who said the rule violated their religious freedom. The Catholic Church opposes artificial birth control.