Prospects for a $10 million Virginia contribution to Metro subway construction improved sharply today as State Senate leaders predicted quick approval of the appropriation and a spokesman for Gov. Mills E. Godwin hinted the governor may drop his opposition to it.

Godwin vetoed a similar appropriation last year and has been extremely critical of the subway project. But John H. Wessells, Godwin's press secretary, said today that the governor is willing to "take a different look" at the measure if it is tied to a ceiling on overall costs for the subway and a lid on operating deficits for the entire Metro transit system.

If those steps are taken, Wessells said, Godwin would "be more amenable to" the Metro appropriation than he was last year.

"We've always said that Metrorail was a part of the Northern Virginia transportation system," he said.

Wessells' comments, which appear to indicate a change in Godwin's attitude, should allay some of the fears that Northern Virginians have expressed about changes for approval of the measure.

Senate Majority Leader Adelard L. Brault (D-Fairfax) said earlier today he was confident that budget amendments restoring the $10 million to the state's biennial budget would win final legislative approval later this week in the Senate. Brault also conceded he was fearful of a Godwin veto again this year.

Although Senate Finance Committee Chairman Edward E. Willey (D-Richmond) declined to comment publicly on the likelihood of Senate approval of the budget amendements, he did say today that the measure probably will pass the Senate without a fight. "I don't think there is going to be any fight because we've got something in there for everybody," he said.

Others on a finance subcommittee that met here last night said the group approved amendments to the House version of the budget bill but did not touch the Metro appropriation and that Willey would not allow the full Finance Committee to vote any other amendments when it meets Tuesday morning.

"We got it resolved on all sides," Willey said today when asked about the likelihood of a dispute between the House and Senate over the budget. Willey, a member of the Senate's conservation faction, led the fight last year over the Metro appropriation and is considered as the legislator closest to Godwin on financial matters.

There has been widespread speculation among legislators here that Godwin may have changed his position on the subway after talking with U.S. Secretary of Transportation Brock Adams. In approving construction of Interstate Rt. 66 between the Capital Beltway in Fairfax County and the Potomac River, Adams said on Feb. 1 Godwin "had indicated to me his full support and continuing cooperation in completing the Metrorail system in Virginia."

At the time spokesmen for Godwin refused to comment directly on Adams' statement and cited a Jan. 13 letter from Godwin to William T. Coleman, Adam's predecessor in the Transportation job. In that letter Godwin had said he was committed to eight "specific conditions" laid down by Coleman for I-66 construction but added he was "not able to bind the commonwealth with respect to future state governmental decisions."

Del. Carrington Williams (D-Fairfax), one of four Northern Virginia legislators with whom Godwin was scheduled to meet today, said he was attempting to develop an amendment that would place some limit on costs of the Metro subway and its deficits. Although Brault canceled the meeting with the governor, Williams noted that Godwin "hasn't said 'yes' and he hasn't said 'no'' to his approach.

"I'm just trying to salvage the best I can out of a bad situation," Williams said.

Although the $10 million contribution from the state would be but a minor part of the Northern Virginia share of Metrorail construction, now estimated at $270 million, Northern Virginia legislators here are fighting bitterly over the appropriation. They contend that Virginia has an obligation to shoulder some of the subway's costs and note that the $10 million comes from a portion of the state's highway budget that already is earmarked for mass transit purposes.

In the past, Godwin has referred to the proposed 100-mile subway as "unfeasible" and once called it a "boondoggie." But today, Wessells noted that the state will have given a total of about $135 million to the Metro system, if the I-66 route is built and certain highway funds are diverted to the subway.

Despite Adams's approval of the route, Brault said today that a lawsuit over the route is likely and the degree of U.S. support in fighting the case may depend on Godwin's action on the $10 million.

In the House Finance Committee today, a gasoline tax measure designed to raise money to pay Northern Virginia's share of Metrorail costs and Metrobus operating deficits was stymied. The bill to authorize a 4 per cent gasoline tax has the support of virtually all the Northern Virginia legislators, it was referred to a subcommittee that is supposed to meet Tuesday to come up with something acceptable to the rest of the committee.

Today's committee debate was in most ways a rerun of last year's when the measure was passed contingent on approval by all five Northern Virginia jurisdictions. Fairfax City refused to approve the tax, thereby scuttling the tax for the other four. This year's proposal is to amend the existing law to permit the localities to adopt the tax independently.