Mitt Romney predicted President Obama would back down on a rule requiring religious-affiliated organizations to offer birth control or "suffer enormous consequence."

"The White House has shown its hand already. This effort is an outrageous assault on religious conscience on this country," Romney said Thursday on the Fox Business Network. "They are going to have to retreat or suffer enormous consequence.

"Ultimately, they will retreat, as forced by the Supreme Court or by the next election, if they don’t retreat now on their own," he continued. "The assault on religious liberty in this country is an area with great energy, support and passion behind it. It is something I share. We have found from liberals across the country an effort to impose their will on religious organizations and the population at large, and that is something we have to fight at every turn."

Romney's comments come as the White House battles criticism from Republicans, conservative groups and some Democrats over the mandate, which requires some religious organizations to cover contraception in their employees’ healthcare plans.

The White House — along with Romney rivals Newt Gingrich and Rick Santorum — has pointed out that its rule is similar to one put in place by Romney when he was governor of Massachusetts.

The Romney campaign fired back on that charge.

"On his first day in office, Mitt Romney will eliminate the Obama administration rule that compels religious institutions to violate the tenets of their own faith. We expect these attacks from President Obama and his liberal friends. But from Newt Gingrich and Rick Santorum, it’s a clear indication of desperation from their campaigns," said Romney spokeswoman Andrea Saul in a statement Wednesday.