The House yesterday gave a strong indication that Congress' $3 billion quick-fix plan to subsidize home buying may never become law, as House Republicans fell back in line with President Reagan to vote against the anti-recession legislation.

The House approved the conference report on the urgent supplemental appropriations bill, which includes the housing subsidy program, and sent it to the Senate for action. But in an earlier test vote, a Republican-backed effort to remove the housing plan was defeated by a 257-to-155 vote--enough to preserve it for now but less than the two-thirds necessary to override a threatened presidential veto.

House members also voted overwhelmingly to limit the amount of income senators can earn from speeches or other outside activities to $18,200, in retaliation for a Senate amendment to repeal a $75-a-day tax deduction for Washington living expenses that senators and congressmen can claim without substantiation.

This confrontation between the House and Senate puts another obstacle in the path of final passage of the "urgent" appropriations bill, which, in addition to the housing money, provides funds for a variety of mostly minor federal agencies to finish out the fiscal year. If the Senate doesn't approve limiting its own outside income, the issue would have to be negotiated or the bill could go back to conference.

The housing subsidy plan, involving federal payments of 4 percentage points of mortgage interest rates for moderate-income buyers of new homes, was originally approved in somewhat different forms by more than two-thirds of both the House and Senate.

Reagan, however, has threatened to veto any housing "bailout" bills as too costly and as bad precedent for other beleaguered industries. Republican sponsors of the legislation still hope to convince the president to sign the final conference compromise as a jobs stimulus plan, saying that employment was its primary function rather than propping up the devastated housing industry.

But David Stockman, director of the Office of Management and Budget, on Tuesday made it clear in a letter to Republican leaders that the compromise version is "particularly unacceptable" to the administration and urged that it be defeated on the House floor.

Rep. Trent Lott (R-Miss.), the minority whip, headed the move to defeat the conference report on a procedural vote, so the housing portion could be removed. The vote to do so was generally along party lines.

While a majority of Republicans voted for the housing program last month, only 41 voted with the majority on yesterday's test vote.

"The Republican party wants to back away from housing support," said Rep. Peter Peyser (D-N.Y.) before that vote. Because of the president's veto threat, the Republican members are all "running for cover," he said.

The only expressed opposition to limiting senators' outside income came from those who argued it would bog down the appropriations bill with an unresolved internecine struggle. The final vote on the motion was 381 to 29.

According to a Democratic Study Group paper, 58 senators made more than $18,200 last year in outside income.

Rep. Vic Fazio (D-Calif.), author of the amendment, said that in 1981 senators made a total of $14 million in outside income, more than double the $6 million in official Senate income they received.

Area members voting to send back the conference report included Maryland Republican Marjorie Holt and Virginia Republicans Thomas Bliley, M. Caldwell Butler, R. W. Daniel, J. Kenneth Robinson, William Wampler and G. William Whitehurst.

The only area members voting not to limit senators' outside income were Holt and Steny Hoyer (D-Md.).