The House Ways and Means Committee yesterday approved, 32 to 3, a bill to rescue the Social Security program, change the way the government reimburses hospitals under Medicare and extend unemployment benefits.

Democratic members broke into cheers as several Republican conservatives, including Rep. W. Henson Moore (La.), lined up behind the omnibus measure. The three opposing the bill were Bill Archer (R-Tex.), Philip M. Crane (R-Ill.) and Richard T. Schulze (R-Pa.).

The committee approved the extension of unemployment benefits after Democrats agreed to chop $200 million out of a proposal that Republicans and the Reagan administration said was far too costly.

The committee also agreed by voice vote to give all recipients of supplemental security income or aid to the blind, aged and disabled a $20 increase ($30 for couples) on July 1, 1983, to compensate them for a planned six-month delay in this year's cost-of-living increases.

Republicans complained that the SSI increase would cost $3 billion over the next five years, about $500 million more than the administration proposal, but their substitute to shave this was beaten, 19 to 12.

Committee leaders hope for floor action on the big bill next week.

The $165 billion Social Security rescue program, involving both tax speedups and spending slowdowns, was worked out Tuesday.

The hospital reimbursement plan involves fixing in advance what Medicare will pay hospitals in given areas for given services. Under current law they are simply reimbursed for their costs.

In a series of bipartisan amendments, the committee agreed to:

* Set different rates for nine separate regions of the country, instead of national rates;

* Phase in the new system in three years;

* Phase out the return on equity received by for-profit hospitals under Medicare;

* Make hospital capital costs incurred after March 1, 1983, subject to a prospective-payment system still to be worked out;

* Order a major study on possible use of the prospective-payment system for physicians treating Medicare patients.

Under the unemployment insurance compromise offered by Rep. Bill Frenzel (R-Minn.), long-term jobless workers in some high-unemployment states who have already exhausted up to 55 weeks of regular and special extended benefits will be eligible for up to 10 more weeks, a total of 65. For others the maximum would be 63 weeks.

Previous estimates suggested the extension would cost around $2.5 billion, or perhaps somewhat more. Frenzel said his amendments, which basically cut two weeks off the extra weeks the states could provide under certain conditions, would reduce these estimates by $190 million to $210 million.

A Frenzel proposal to allow states to impose a means test for unemployment benefits was beaten, 17 to 16, with only a handful of Democrats in favor. Rep. Harold D. Ford (D-Tenn.) protested that unemployment insurance has never been a charity program but was set up in 1935 to replace jobless workers' lost wages and keep up their purchasing power.

The unemployment package would allow states to use part of their jobless-worker funds to provide health insurance benefits if the worker wished.