The National Women's Law Center (NWLC) also criticized the proposed plan. "The debt ceiling deal averts the disaster of default but at a painful and unfair price," Nancy Duff Campbell, NWLC co-president, said in a statement.

Both organizations indicated they are particularly wary of the idea of a so-called "super committee" composed of 12 members of Congress tasked with putting together recommendations for a $1.5 trillion deficit-reduction package that would be presented to Congress later in the year.

According to O'Neill, the so-called "super-committee" included in the latest plan would "make it more likely than not that the ultimate product will include cuts in Medicare, Medicaid and possibly Social Security."

NWLC, a nonprofit organization with a special emphasis on the legal rights and concerns of low-income women, warned against a committee that would "have the authority to consider cuts to all spending programs."

Duff Campbell urged in a statement that House Speaker John BoehnerJohn Andrew BoehnerDemocrats eager to fill power vacuum after Pelosi exit Stopping the next insurrection Biden, lawmakers mourn Harry Reid MORE (R-Ohio) "should not be allowed to prevail" at keeping tax increases for the wealthy off the table.

NOW has weighed in on the deficit negotiations before, warning Obama and congressional leaders to leave Social Security, Medicaid and Medicare out of the debt deal and calling for more consultation with women leaders in Congress.