A drawing of a proposed Metro stop at Tysons Corner. (Gerald Martineau/THE WASHINGTON POST)

The board had previously voted to make its project labor agreement mandatory for the second part of the rail line, also called the Silver Line. But on Wednesday the board voted to pull back that version and instead put in place an agreement that will give bidding firms a 10 percent incentive in their scoring to win the deal if they implemented a union-friendly labor deal.

The changes came about mainly because of a push from Virginia lawmakers who have introduced legislation saying they would not support the state of Virginia giving the promised $150 million to the second part of the Dulles project if there was a mandatory project labor agreement in place.

MWAA oversees operations at Reagan National and Dulles International airports, along with the construction of the new 23-mile extension of Metrorail line through Tysons Corner. The first phase of the project is under construction and expected to open to passengers in 2013. MWAA expects to have eight firms bid on building the second part of the Dulles rail line and then reducing that list to a top five. MWAA would then pick a contractor to build the second phase by January 2013.

MWAA officials say 75 percent of the construction is completed. They expect it to be done on time, but have said the project could be as much as $150 million over budget.

Outside consultants for MWAA also put out revenue projections for the Dulles Toll Road in coming years. Their results show revenue projections are “slightly lower” than previous projections in 2012 through 2028. The toll revenue is used, in part, to help pay for the Dulles rail construction.

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An earlier version of this story misstated the year in which the first phase is scheduled to open and the conrtactor for the second phase will be picked. It has been corrected.