A $66 billion highway and mass transit bill that the House Public Works Committee has approved began to shrink yesterday under pressure from the Carter administration, another House committee and Proposition 13.

The occasion was a mark-up session in the House Ways and Means Committee, which has to approve that part of the bill that would permit the financing of four years of highway projects with six years of revenues from the Highway Trust Fund. Such an approach would enable Congress to finance the highway programs intact without forcing an unpopular gasoline tax increase. The highway trust fund is mainly financed by the federal gasoline tax.

By the time the session closed yesterday, no votes had been taken but Public Works subcommittee chairman James J. Howard (D-N.J.) had promised to amend the bill downward by $5.6 billion.

Furthermore, Howard had agreed that he would support a technical amendment under which all highway programs would share equally in cuts if the trust fund does not produce enough revenue. As presently written, only the Interstate Highway program - about a third of the total - would be affected.

"Howard knows this bill will get killed on the floor by that Proposition 13 crowd," one knowledgeable congressional source said, referring to nervous congressmen seekin to make taxcutting their own issue. "If he promises cuts here, at least he'll be able to decide which programs get cut and which ones survive."

A key aide to Transportation Secretary Brock Adams was also pleased by the developments. "This brings us closer to the Senate bill and gives us something we can work on in conference," he said. Three equivalent bills Senate passed earlier by the Senate would total about $50 billion for four years.

In recent weeks the Carter administration has begun vigorous, lobbying against the public works bill, which is $20 billion higher than the administration proposal. Robert S. Strauss, the president's anti-inflation adviser, met with the road-building lobby and called the bill inflationary. Adams has labeled the bill "pure pork barrel" and has called several members of Congress and met with editorial page editors to register opposition.

The attack has centered on the funding proposal under which six years of Highway Trust Fund revenues would be used for four years of highway projects. The Ways and Means Committee must approve extension of the trust fund if its 22-year existence is to continue.

Two members of Ways and Means, Reps. Sam Gibbons (D-Fla.) and Barber B. Conable R-N.Y.), have proposed an amendment to limit highway expenditures in one year to the revenues available in the trust fund.

If the public works bill is approved as written, Gibbons said, "by 1985 there will be $30 billion in unpaid bills" because the trust fund will be empty but road programs will have continued. Public Works Committee staff members disputed that figure.

Rep. Bill Frenzel (R-Minn.) responded: "I do not believe in borrowing from the future. With all due respect [to the Public Works staff]. I'd like to have these fellows keep my golf scores."

Howard told the Ways and Committee he was "extremely opposed" to the Conable-Gibbons amendment because, he said, there is already adequate protection for the fiscal integrity of the trust fund, because the amendment would hold highway programs below levels the fund could sustain and because the administration, not Congress, could control highway spending. Under the amendment, the secretary of transportation would determine the trust fund revenues available.

Howard said he will offer $5.6 billion in cuts. The biggest cut would be $2 billion cut of the bridge replacement program, which on an annual basis was increased in the public works bill from $500 million this year to $2 billion next year. That program has been most heavily attacked as pure pork. CAPTION: Picture, REP. JAMES J. HOWARD . . . promised to pare $5.4 billion