Congress yesterday sent President Reagan an "urgent" supplemental appropriations bill that includes a $3 billion quick-fix housing program, after the House backed down from its amendment to limit the annual outside income of senators to $18,200.

Reagan is expected to veto the legislation because of his opposition to the housing program, Congress' only piece of anti-recession legislation this year.

If the bill is vetoed today, the House plans a vote to try overriding the veto before recessing today for two weeks.

The housing provision would offer interest-rate subsidies of 4 percentage points of a mortgage on newly built homes for some moderate-income families. The rate could go no lower than 11 percent, and the subsidy would last five years. The home buyer would have to repay the subsidy when the house is sold or refinanced.

Proponents of the measure have billed the legislation as a stimulus to create jobs and get the devastated home-building industry back to work. But the administration has argued that it is a bailout that would not have a strong impact on jobs but would lead to special requests for assistance from other industries hit by the recession.

Both chambers approved the housing measure overwhelmingly, but sponsors of the legislation have said it would be difficult to get enough Republicans to go against Reagan after a veto to muster the necessary two-thirds' majorities for an override.

Before final action yesterday the House and Senate spent a day trying to stare each other down over differences on how to proceed with the bill's controversial elements, with the emergency funding in the measure being held hostage to the deliberations.

The House finally blinked, after originally insisting that the housing and outside-income issues should be held over until next month. Yesterday morning the House sent the Senate a stripped-down bill providing only emergency funding to carry various programs and agencies through the House recess.

House Democratic leaders had vowed to fight the housing battle next month, and congressional aides said they planned to organize a grass-roots campaign during the recess designed to pressure Reagan to sign the bill or Republican congressmen to override a veto.

Sen. Richard G. Lugar (R-Ind.), original author of the bill, said the delay would hurt its chances because this year's construction season is almost half over, leaving less justification for the measure the longer it is held up.

When the Senate balked at passing the stripped-down bill, the House was forced back to the version approved by a House-Senate conference committee, and had to delete its amendment on senators' income.

That amendment had been tacked on in retaliation for a Senate amendment to repeal a $75-a-day tax break that members of Congress can take without substantiation for living expenses here.

House members said it was not as important to senators, because they had no limit on the amount of income they can earn from speeches or other outside activities. The House limits the outside income of its members to $18,200 annually.

The $8.9 billion urgent supplemental bill includes $2.4 billion for sewage construction grants, $1.3 billion in student loans and money needed to pay salaries for thousands of federal workers.

If a veto is sustained, there are contingency plans to bring up an urgent appropriations bill stripped of the housing components, in hopes of quick passage of funding for emergency needs.