Senate Republican Leader Mitch McConnell said he'll push to overturn the mandate because it is another example of government meddling, reported the Washington Post.
President Obama backed down on the requirement that religious-affiliated employers, like Catholic hospitals or colleges, cover birth control in their insurance plans. A new tweak of the rule said the employees would be offered free coverage directly from their insurer but employers wont have to provide or pay for it, reported Star Tribune.
The plan should drive up costs because birth control, along with other preventative care measures, is less costly than pregnancy.
Opponents say that unless makers stop charging for contraception, the cost will likely be passed to employers regardless.
Some Catholic groups supported the change, but others continued to say it attacks their religious freedom. This theme is also being used by the Republicans.
"There is no compromise here," said GOP presidential hopeful Rick Santorum, a Catholic, reported by the Washington Post.
White House chief of staff Jacob Lew defended the newest plan as the best possible compromise in order to provide women access to contraceptives and respect employer's religious freedoms.