As the Loudoun County Board of Supervisors prepares for a final work session Friday to discuss the extension of Metro’s Silver Line, county leaders have made it clear that, despite a recent request by three supervisors for an additional deadline extension, a final vote on whether to commit to the project will take place Tuesday.

The board faces a Wednesday deadline to decide whether to opt in to the second phase of the construction, which would bring Metrorail to Dulles International Airport and eastern Loudoun.

Shortly before a June 18 work session, supervisors Kenneth D. Reid (R-Leesburg), Geary Higgins (R-Catoctin) and board Vice Chairman Janet Clarke (R-Blue Ridge) distributed a list of 21 items that they said should be addressed before the board casts a final vote on the project. Among the items was an unofficial request to extend Loudoun’s current decision deadline by five months, to Dec. 1.

“We believe that if [the Metropolitan Washington Airports Authority], Fairfax County and [Washington Metropolitan Area Transit Authority] truly want to partner with Loudoun County on this project, they will take the time to work through the construction and funding details on this project,” the memo said. “This is not much to ask for in return for a lifetime of commitment from our citizens.”

Despite the proposal, Board of Supervisors Chairman Scott K. York (R-At Large) released a statement Friday emphasizing that the board had not made a formal request for an additional deadline extension and had no plans to do so.

“For clarity’s sake, the Board of Supervisors has not, and I repeat, has not, requested an extension,” the statement said. “A vote to opt in or opt out will occur on July 3.”

Four members of the board — supervisors Matt Letourneau (R-Dulles), Shawn Williams (R-Broad Run), Ralph Buona (R-Ashburn) and York have expressed support for the project. Supervisor Eugene A. Delgaudio (R-Sterling) has voiced emphatic opposition throughout the rail discussions. The positions of the remaining supervisors — Reid, Higgins, Clarke and Suzanne Volpe (R-Algonkian) — are uncertain, appearing to have fluctuated between conditional support and skeptical concern.

After the release of the memo listing 21 items for opt-in consideration last week, Reid took a step back from the request for more time, clarifying in a statement that the list was “by no means an ultimatum of necessary conditions.”

Although he supports an extension of time to “work out certain particulars,” he said, if they are not resolved before the deadline, he does not think a “hard date” of Dec. 1 “is by any means necessary or desired to accomplish that.”

In recent weeks, supervisors have examined several possible funding sources for the project, including establishing special tax districts, instituting a commercial and industrial tax, and a combination of the two. The board has focused in particular on the possibility of a tax district, proposed by Williams, that would concentrate on commercial properties and undeveloped land in the immediate vicinity of the Metro stations.

In an e-mail newsletter to constituents, Buona said that he was “cautiously optimistic” about the board’s stance on the second phase of the construction.

In the newsletter, Buona noted that a majority of Loudoun residents who addressed the board at a June 4 public meeting were in favor of the rail extension. More than 1,000 e-mails his office received were also “overwhelmingly in favor” of the project, he said.

Buona, like several of his colleagues, has expressed a desire to fund Loudoun’s roughly $270 million share of the construction costs without placing a financial burden on county taxpayers or dipping into the county’s general fund.

“I believe we are very close to having that plan finalized and that it will be palatable to a majority of the supervisors,” Buona said in the newsletter.

Letourneau said in an interview Tuesday that he was less confident about where the board stood but that he hoped the final work session might pave the way to majority support.

“I still think it’s really up in the air. There’s four of us who are going to support the project. I think it’s safe to say there’s three who are not, and two are in the middle,” Letourneau said.

He said he hoped that defining a financial plan would give the skeptical supervisors “a reason to vote for the project, but there’s certainly no strong indications either way.”

It isn’t often that a major project makes it to a final vote without a clear indication of how the board will proceed, Letourneau noted.

“This may be one of those situations,” he said. “It certainly adds to the drama.”