After months of debate and negotiation over Metro’s Silver Line rail extension, all eyes will be on Loudoun County on Tuesday as the Board of Supervisors decides whether to commit to the long-planned project.

The board faces a Wednesday deadline to opt in to the second phase of construction, which would bring Metrorail to Dulles International Airport and eastern Loudoun. The Silver Line’s first phase, which is under construction, runs through Tysons Corner to Wiehle Avenue.

After a final work session Friday to discuss a financing plan for Loudoun’s share of the costs — about $270 million toward construction, and about $17 million to $20 million a year beginning in 2019 to support operating costs — it appears that the board may have the five votes needed to secure majority support for the project.

Four members of the board — Chairman Scott K. York and Supervisors Matt Letourneau (Dulles), Ralph Buona (Ashburn) and Shawn Williams (Broad Run) have consistently expressed support for the project. Supervisor Kenneth D. Reid (Leesburg), who has voiced concerns about financing, appears to be leaning toward backing it.

The positions of three other supervisors — Suzanne Volpe (Algonkian), Geary Higgins (Catoctin) and Vice Chairman Janet Clarke (Blue Ridge) — remain uncertain. Supervisor Eugene Delgaudio (Sterling) has emphatically opposed the project.

Several members of the board, including Reid, have focused on the need to identify a funding plan before committing to the second phase of the Silver Line. At Friday’s meeting, the supervisors supported a plan proposed by Williams that would fund Loudoun’s share of the project through a hybrid tax district surrounding the Metro stations. The proposed district encompasses commercial properties and undeveloped land, almost entirely excluding existing residential properties.

Loudoun’s nine-member, all-Republican board was elected in November on a unified platform to support fiscal discipline and economic development in the county. When it comes to the Silver Line, those two campaign promises have sparked conflict: Opponents have balked at the price tag and voiced fear that taxpayers would foot the bill, while supporters of the project, including many in Loudoun’s business community, have emphasized the economic benefit of bringing Metro into the county.

Although both sides stepped up their public outreach efforts as the decision deadline approached, a clear majority of Loudoun residents who addressed the board at a June 4 public meeting spoke in favor of the Silver Line.

Initial discussions between the Metropolitan Washington Airports Authority, the state, and Loudoun and Fairfax counties about the second phase of the project stalled over the airports authority’s inclusion of a union-friendly contracting provision in the deal. Early last month, the authority voted to eliminate the project labor agreement after Gov. Robert F. McDonnell (R) threatened to withhold $150 million in state funding.

The authority’s vote was welcome news in Loudoun, but concerns about how to finance the county’s share of construction and operating costs remained a subject of debate among the supervisors.

The financing proposal from Williams received eight votes at Friday’s work session, with Delgaudio casting the lone opposing vote. The financing plan is contingent on a vote to opt in to the second phase of construction at Tuesday’s meeting, meaning that the supervisors’ acceptance of Williams’s plan does not necessarily indicate support for the rail project.

Letourneau said the discussion Friday was generally positive, aided by the fact that Williams’s plan alleviated the concerns of supervisors who did not want to raise taxes on residents.

“Judging from the tenor of the questions and the discussion that the board was having, I’m pretty optimistic that we’ll end up being part of the Metro project,” Letourneau said.

But given the back-and-forth that has often characterized the debate, he added, there is no guarantee until a final decision is made. “Until we actually take the vote, anything can happen,” he said.

York and Loudoun County Attorney John R. Roberts confirmed Friday that the board must cast a positive vote to remain a funding partner in the second phase of the project. If the board did not vote before the Wednesday deadline, or if a tie vote were cast, Loudoun would effectively opt out of the second phase.