Labor-led opposition to President Reagan's recommended budget cuts began to take concrete shape yesterday as the United Mine Workers announced a two-day protest strike and a giant coalition of unions and other groups revealed its plans to resist the proposals.

The mine workers said they will strike March 9 and 10 to demonstrate their anger over proposed reductions in the trust fund that aids victims of black lung disease. The new "Budget Coalition" that presented itself at a news conference at AFL-CIO headquarters here has the broader goal of fighting most of the cuts Reagan wants to make in social welfare and jobs programs.

Yesterday's events appeared to signal an end to the relative honeymoon the new administration has been enjoying since Reagan unveiled his economic plan 10 days ago. It is the first major organized opposition to have emerged.

Lane Kirkland, president of the AFL-CIO, read the coalition's initial policy declaration for reporters and television cameras. "These [administration] proposals do not set forth a period of belt-tightening shared by all, after which America can again grow and prosper at all levels of our society," Kirkland said. "Instead, many vital programs are marked for extinction and others will be hopelessly crippled."

Reagan's proposed cuts "could wreak great damage to the fabric of this nation," Kirkland declared, insisting that the president's program "will not solve" the problems of high inflation, high interest rates, high energy costs and high unemployment.

The Budget Coalition has a diverse membership that includes the United Auto Workers, the National Education Association, the League of Women Voters, the National Association for the Advancement of Colored People, the Consumer Federation of America, the American Agriculture Movement, the U.S. Catholic Conference, the National Council on Senior Citizens, the National Urban League and the Sierra Club. In all, 157 different groups signed the coalition's initial statement.

After yesterday's news conference, representatives of member organizations met to discuss cooperative lobbying efforts to save the programs they care about. Kirkland said member groups would cooperatively lobby for each other as well as for their own favorite programs

Representatives of a number of member groups spelled out their quarrels with Reagan's plans. One of the most emotional was Marvin Meek, national chairman of the American Agriculture Movement, who told the gathering he had campaigned for Reagan in 34 agricultural states last fall "because he promised to life the grain embargo and return profitability to farming." Meek said his group felt Reagan had abandoned his promises.

The American Federation of State, County and Municipal Employes announced formation of another anti-cuts coalition yesterday, this one aimed solely at protecting the Medicaid program that finances health care for the poor.

Complaining about another aspect of the proposed budget cuts, former commissioner of internal revenue Sheldon Cohen said that the new administration is being penny-wise but pound-foolish by ordering the Internal Revenue Service to reduce its staff.

"The rule of thumb," Cohen told a reporter, "is that $1 spent on the IRS staff has a marginal return of at least 6 to 1" because of extra tax revenues extra agents can collect.

Cohen said that known tax liabilities of more than $10 billion -- probably $15 billion -- exist that are not collectible because IRS doesn't have enough agents to send out.

Last night, however, it was reported that IRS had reached a compromise with the Office of Management and Budget. The staff cuts will be smaller and in return OMB will accept the Treasury Department's higher estimate of how much revenue each agent can collect. This will help the administration to show higher revenue estimates than otherwise, offsetting to some extent the expected revenue loss because of the president's decision to rule out a gasoline tax increase.