RALEIGH, N.C.—A consensus is emerging on how to compensate thousands of men and women sterilized in one of the largest state eugenics programs in the U.S. But North Carolina's budget troubles make it unlikely that the aging victims will get cash payments anytime soon.

A perennial legislative proposal to pay as many as 3,000 sterilized people $20,000 each got a boost this spring after Republicans took over North Carolina's House and Senate following the November elections.

Compensation for victims has long been championed by state Democrats, but the idea gained momentum with the recent endorsement of some high-ranking Republicans who said sterilization was an infringement on individual rights.

"Most of the time, we're thinking from the neck up, but this one started with me in the stomach, the intuition of it all," said Republican Rep. Dale Folwell of Winston-Salem....

North Carolina is among more than 30 states that once sanctioned eugenics; the vast majority of the victims were sterilized either forcibly or with inadequate consent.

The eugenics movement, which gained popularity in the early part of the 20th century, called for sterilizing some Americans who were deemed socially or intellectually unfit. But North Carolina was the rare state that accelerated its program after World War II, amid a backlash against the eugenics practices of Nazi Germany....