The resolution, which was not binding, would have asked all eight members of the congressional delegation to vote against any legislation seeking reductions in federal money spent on Medicare and Medicaid.
A number of senior citizens at the meeting urged council members to approve the resolution.
"We're being swept away by this thing, and it's going to affect a lot of people -- and not just elderly people," said Ernie Crofoot of Bowie, co-chairman of the Senior Citizens Coalition.
"The argument we got is that it's none of our business. And we say that it's everyone's business what's happening to old people."
Charles Culbertson of Towson, a former president of the United Seniors of Maryland, said the proposed cuts in Medicare and Medicaid would represent more than 40 percent of the cuts in spending the federal government is seeking to trim the deficit.
"Forty percent seems to be an unfair penalty to put on old people, who have few resources," Mr. Culbertson said. "The seniors out there cannot afford the cuts that are being proposed. There are no safety nets to pick these people up."
But Councilman William C. Mulford II, a Republican from Annapolis, bristled when some people in the audience suggested that doctors and hospitals are to blame for the problems with Medicare and Medicaid.
"I take great offense at said comments," said Mr. Mumford, who noted that his father is an obstetrician/gynecologist. "I can't tell you how many dinners and breakfasts I missed having with my dad because he put his patients before his family."
Council Chairwoman Diane R. Evans, and council members John J. Klocko III and Bert L. Rice joined Mr. Mumford in defeating the resolution. Council members George F. Bachman and James E. DeGrange voted for the resolution, and council member Thomas W. Redmond abstained.
The council also unanimously approved County Executive John G. Gary's list of applicants to fill a vacancy and alternate member position on the property tax assessment appeal board.
The list of three names for each position will go to Gov. Parris N. Glendening, who will make the selections. The new regular member and alternate member would serve the remainder of the term that started June 1, 1993, and ends June 1, 1998.