Most insurers must meet the requirement by Aug. 1, while qualified non-profit religious groups have another year to comply.
Churches and houses of worship do not have to follow the new rule, released nearly two weeks ago.
Critics of the directive — mainly Catholic and Protestant evangelical leaders — say it infringes on freedom of religion.
And the resulting wave of protests have "clearly taken administration officials by surprise" and may be "politically risky for Obama in a close election year," the Associated Press wrote.
However, the Wall Street Journal cited White House press secretary Jay Carney as saying Thursday that the administration had no plans to reverse course on its decision.
“The decision has been made, and it was made after careful consideration,” he told a regular briefing.
According to the WSJ, the White House also published a blog post by Cecilia Munoz, director of the House Domestic Policy Council, pointing out that "no individual health care provider will be forced to prescribe contraception” and “no individual will be forced to buy or use contraception."
Boehner, meantime, a Catholic, was quoted by the AP as saying Thursday: "I think this mandate violates our Constitution. I think it violates the rights of these religious organizations. And I would hope that the administration would back up and take another look at this."