The House yesterday bowed to public pressure and agreed to repeal a tax break Congress had given itself last year.

The provision repealing the tax break would be attached to a controversial supplemental appropriations bill, which also contains a bailout program for the housing industry and which President Reagan has threatened to veto.

The bill is in conference; the Senate has already voted to repeal the tax break, and the House vote of 356 to 43 came in the form of instructions to its conferees to concur and do the same. Congress would thus return this year to an earlier system by which members can claim a flat $3,000 business deduction each year for the expense of living in Washington.

The new tax break, under which members would have been able to take $75 in unsubstantiated expenses each day Congress is in session--or more if they could document the expenses--meant that last year each member could claim a minimum of around $19,000 in business deductions for living expenses.

Reagan has threatened to veto the supplemental appropriations bill because it includes a $1 billion-a-year program to stimulate new-home sales by subsidizing mortgage interest rates for some moderate-income home buyers. The House and Senate both approved the mortgage subsidy, which would pay 4 percentage points of interest on a new home loan for eligible buyers, by more than the two-thirds majorities needed to override a veto.

The conference committee met late yesterday, hoping to complete its negotiations in time for the House to approve the compromise today. But the conferees ran into a hitch on the housing subsidy, which the two houses had passed in somewhat different form. Staff aides say that if the conferees do not reach a compromise on the subsidy, the issue could be taken up separately again on the floor of the House or Senate.

The overwhelming vote to repeal the tax break came only after the House defeated, by a much closer 218-to-176 vote, a proposal by Rep. John T. Myers (R-Ind.) that would have dropped the $75-a-day guarantee but still allowed members to claim any business deductions they could justify to the Internal Revenue Service.

Because congressmen maintain the homes in their districts as their principal residences, it is technically possible that if treated like everyone else, they could claim all their Washington living expenses as business travel deductions.

The proposal enabled member after member to get up and proclaim that they merely wanted to be treated like any other taxpayer with business expenses.

"I just want to be a normal, ordinary citizen," declared House Minority Leader Robert H. Michel (R-Ill.) in supporting the Myers proposal.

But Rep. Paul Findley (R-Ill.) envisioned deductions for "expensive houses and chauffeurs" in Washington under the plan, saying Congress should not "open the skies" to these kinds of deductions because the issue is "very much on the minds of the American people . . . and something they can understand."

Several members bemoaned the treatment they had received at the hands of the press even with the $3,000 deduction, and others called on their colleagues to stick to their guns in voting themselves the tax break.

"I've watched the House flog itself on this issue and demean itself . . . . You're telling people at home that you are not worth what you are paid," said Rep. Don Young (R-Alaska).

Most Virginia and Maryland members of Congress voted for the Myers amendment, but then voted for the repeal of the tax break. Those voting no on the Myers proposal were Maryland Reps. Roy Dyson (D) and Marjorie Holt (R), and Virginia Reps. Stan Parris, William Wampler and Frank Wolf, all Republicans, with Paul Trible (R) not voting. Rep. M. Caldwell Butler (R-Va.) was the only area congressman to vote no on the tax break repeal.

Meanwhile, the House Ways and Means Committee voted yesterday to start a new system of congressional tax deductions for 1983 and beyond. The measure would let members take any expenses they could justify to the IRS for working in Washington. This plan, essentially the same as the Myers proposal defeated earlier in the day, would enable members to claim food and housing costs, for example, potentially more than the flat unsubstantiated $75 a day the House had just agreed to repeal.