WASHINGTON -- More than 3 million low-income Americans have applied for extra assistance under Medicare's new prescription drug benefit that kicks in Jan. 1.

The Social Security Administration said it considers that a good sign. But an advocacy group said the more important number is how many applicants will actually receive assistance.

The new benefit offers everyone on Medicare drug coverage through a private plan regardless of income or health status. Even critics acknowledge the program is a good deal for the poor.

Officials estimate the subsidy will average about $2,100 for a low-income Medicare recipient. For some, it will cover all their premiums and deductibles.

The assistance will average about $750 for the Medicare population as a whole.

"We are continuing our outreach activities in cities all across the U.S., and we continue to work closely with federal, state and local agencies and groups to let all those who may be eligible know about the help that is available," Social Security Commissioner Jo Anne Barnhart said in a news release.