A controversial Social Security financing bill was cleared for the House floor yesterday by the Rules Committee, 7 to 2, after a long dispute over proposed mandatory Social Security coverage for federal employees.

Debate is to start today. Only nine already specified floor amendments can be offered, the committee ruled.

Whatever happens, the bill will mean higher Social Security taxes for many employees to strengthen the financailly troubled system.

But the tax increase will be even higher if the House approves an amendment by Joseph L. Fisher (D-Va.) to strike out compulsory coverage for 2.5 million federal and about 4 million state, county and municipal employees.

The present maximum tax on a worker, $965 a year, is already scheduled to rise under current law. The bill as written would raise this to $2,588 by 1986 for the highest-paid workers, those making $37,500 or more. However, if Fisher's amendment passes, the maximum tax on the highest-paid taxable workers ($40,200 or more a year) would rise to $2,814 to compensate for revenue that would have been obtained by including federal, state and local government employees. This increase in the tax is incorporated in the Fisher amendment.

Yesterday the 24-member Democratic Steering an Policy Committee, headed by Speaker Thomas P. (Tim O'Neill Jr. (D-Mass.), unanimously endorsed the Fisher amendment and the remainder of the bill.

The House Ways and Means Committee two weeks ago voted 23 to 12 to bring all federal, state and local government workers under Social Security on Jan 1, 1982. It envisioned supplementary pension systems to keep their total benefits about the same. However, by eliminating certain types of "double dipping" and unfair receipt of weighted benefits, the new system was expected to save several billion dollars a year for Social Security.

Federal employee unions, fearing that their members may end up worse off when the final system is put together, have waged a powerful campaign against mandatory Social Security coverage and are strongly backing the Fisher proposal. Rules Committe member Joe Moakley (D-Mass.) said, "The count is that Fisher is going to pass."

The whole bill may face trouble because of the distasteful burden of new taxes, but lawmakers say there isn't any other way to keep the system solvent.

In the Senate, meanwhile, Gaylord Nelson (D-Wis.) was readying a proposal that would throw a larger burden of the new taxes on business firms, by making them pay the Social Security tax on the first $50,000 of an employee's earnings in 1979 and $75,000 in 1985 - while the employees themselves were paying on a smaller portion of their wages. Nelson has cut back his original $100,000 proposal because of objections in the Senate Finance Committee.