Clearing the way for talks to continue this week on the Metrorail extension to Dulles International Airport, the Fairfax County Board of Supervisors on Tuesday endorsed the outlines of a compromise between the local, state and federal players paying for the multibillion-dollar project.

The deal, brokered by U.S. Transportation Secretary Ray LaHood, is designed to trim hundreds of millions of dollars from the $3.5 billion cost of the second phase of the rail line from Wiehle Avenue to Loudoun County, in part to slow future increases in rates on the Dulles Toll Road.

Fairfax supervisors initially balked at one element of LaHood’s plan that would require the county to pick up the estimated $83 million cost of the planned Route 28 Metro station. Under the resolution approved Tuesday, the county would agree to pay for the station – and two Metro parking garages – as long as the county government receives sufficient financing, including loans from the federal government.

Board of Supervisors Chairman Sharon Bulova (D) said the board’s endorsement, after almost an hour of debate, is meant to “make this action as cost-neutral as possible” for the county and to ensure that Fairfax does not “fund an inequitable share of the project cost.”

Supervisor John C. Cook (R-Braddock) said the board’s position recognizes the reality that “as much as we might want someone else to write us a check, they are not going to.”

Last week, the rail line cleared a major hurdle when Washington’s airports authority reversed course and embraced a less expensive aboveground station for Dulles after months of pressure from the region’s elected officials.

For LaHood’s compromise to hang together when talks continue Friday, it requires support from all of the local, state and federal investors. A draft agreement counts on Virginia, for instance, to contribute at least $150 million. Virginia’s Gov. Bob McDonnell said Tuesday that he would consider putting up the money if the state secures greater representation on the board of the airports authority, which is overseeing the rail line project. Virginia’s governor appoints five of 13 members to the board; Maryland and the District have a combined total of five members; and the president appoints three.