WASHINGTON, July 29 - Martha Alls, whose father worked at a uranium plant in Paducah, Ky., thought she would never see the day when the government would pay.

 But Ms. Alls's mother, Clara Harding, will receive a check for $150,000, possibly as early as Tuesday, in a federal plan to compensate sick nuclear weapons workers or their survivors.

 The United States Department of Labor is running the program, which will officially begin on Tuesday. Elaine L. Chao, the secretary of labor, calls it "an absolute priority."

 But the government has not always had that attitude.

 Before Joe Harding died of cancer in 1980, his bones were found to contain up to 34,000 times the expected concentration of uranium. Yet while he lived, Mr. Harding was denied compensation because official records showed he was exposed to only small levels of radiation.

 The Energy Department has identified 317 sites in the nation that employed more than 650,000 people in jobs related to nuclear weapons during the cold war. The agency at first thought 3,000 to 4,000 workers might receive compensation, but the accuracy of that estimate is unclear.

 The Congressional Budget Office estimates the program will cost roughly $2 billion over a decade.

 Mr. Harding was among those who pressed the Energy Department to acknowledge that workers were getting sick from bomb-making components, and his widow and daughter took up the fight.

 The government finally conceded two years ago that many workers who built America's nuclear weapons probably became ill because of exposure to radiation on the job. Congress approved the compensation program last year.

 The law provides medical care and $150,000 to sick workers exposed to radiation, which can cause cancer, and silica or beryllium, which can cause lung diseases.

 For certain workers at sites that kept poor records, the government will presume that particular cancers linked to radiation were work-related.