About 3.1 million people have applied for the extra assistance the government will give poor people when Medicare's (search) prescription drug benefit kicks in Jan. 1, the agency said Thursday.

Under the coming drug benefit, everyone on Medicare can get drug coverage through a private plan regardless of income or health status. While there has been some debate over the adequacy of the new benefit, even its most outspoken critics acknowledge that the program is a good deal for the poor.

Officials estimate the subsidy will average about $2,100 per low-income Medicare recipient; for some, it will cover all of their premiums and deductibles. For the Medicare population as a whole, the subsidy will average about $750 per recipient, analysts say.

The Social Security Administration said it viewed the number of applications as a good sign.

We're really pleased with where we are, but my main message today is we're not done yet," said Jo Anne Barnhart, commissioner of the Social Security Administration.

One advocacy group said the number of applications was meaningless. Government agencies reject scores of applications for assistance in other programs, said Robert Hayes, president of the Medicare Rights Center in New York City.

"How many applied is kind of irrelevant compared to how many will get assistance," Hayes said. "If they reported 3 million people enrolled in the extra help today, we would be opening the champagne bottles."

Barnhart said the agency was still reviewing most of the applications, and did not yet know how many would get approved.

The additional help is for those whose incomes are at 150 percent of the poverty level and below — about $1,200 a month for an individual or $1,600 a month for a couple. The value of assets, such as savings accounts and investments, must be less than $11,500 for singles or $23,000 for couples.

About 15 million people are believed to be eligible for the extra help with their prescription drug expenses. About half will be automatically enrolled because of their participation in other government programs. The other half must apply.

Barnhart said about 19 million applications were sent out with the knowledge that many of the people who got them would not be eligible. Officials said they believe about 7.5 million of the people who got applications are eligible for the benefit.

The last wave of applications went out in mid-August. The SSA made telephone calls to many of those who did not initially respond to the letters.

"If you look at it in terms of the 19 million people, it's a tremendous response rate for a mailing," Barnhart said. "If you look at the subgroup in terms of who we thought would be eligible, it's a very good number."