Fairfax County is expected Tuesday to approve funding for the second phase of Metro’s new Silver Line, but the project could be in jeopardy because of disputes over its cost and the role of unions in constructing it.

On Thursday, Virginia legislators backed away from providing $300 million to help pay for the second leg of the 23-mile Metrorail line to Dulles International Airport and Loudoun County. State officials have also objected to a plan to give incentives to contractors who use unionized labor. Plus, supervisors in Loudoun have expressed reluctance about paying their share — about $260 million.

The roughly $2.8 billion first phase of the Silver Line is under construction through Tysons Corner to Reston and is expected to be completed next year. Construction of the $2.7 billion second phase is expected to start in January, and for the past year officials have been caught up in discussions over how to contain costs and pay for it. The Phase 2 estimate assumes that Loudoun and Fairfax counties would pay for construction of five parking garages and a Route 28 rail station.

On Tuesday, Fairfax is expected to vote on whether to contribute up to $498 million, but Loudoun has until July to reach a decision.

Virginia had pledged $150 million toward Phase 2 as part of a compromise negotiated by the federal government, but members of the Metropolitan Washington Airports Authority board, which is overseeing the project, had been pushing for more money from the state to help offset expected increases in fees along the Dulles Toll Road.

More than half of the cost for Phase 2 is projected to be paid for by Dulles Toll Road revenue. One-way rates are expected to rise from $2.25 to $4.50 as early as next year. By 2018, tolls for that one-way trip could jump to $6.75.

Robert Brown, a member of the airports authority board, said the additional $300 million from the state is unlikely now:

“The message from the Republicans [in Richmond]: Toll payers, pound salt.”

Virginia Secretary of Transportation Sean T. Connaughton said that the state never offered more than $150 million, something he has been telling legislators since at least March 10, the last day of their regular session.

“We scraped together the $150 million,” Connaughton said.

But Sen. Janet D. Howell (D-Fairfax), a budget negotiator who has pushed for money for the Silver Line, said the administration recently offered as much as $200 million.

Connaughton said Monday that if Fairfax or Loudoun pulls out then negotiations for Phase 2 must start over because every agreement includes both counties.

“We’re going to be back to square one,” he said.

Another point of contention has been the seating of additional members on the airports authority board, who were appointed by Virginia Governor Robert F. McDonnell (R).

On Monday, Connaughton said he would not consider more money until Virginia’s members are seated, other members who should not be on the board are removed and the board removes the labor language.

“Major movement needs to be made . . . before I could ever envision giving more money,” he said. “They’re not going to get the $150 million if they continue to do what they’re doing.”

But Loudoun Sen. Mark R. Herring (D) said it “is troubling and disturbing to hear the secretary say the $150 million is now something that might come off the table. It’s critically important for Loudoun to have the rail project extended not only to Dulles but into the county.”

Many of the newly elected supervisors in Loudoun had been concerned about the high cost of the project. The additional $300 million from Virginia might have given them the confidence to put up their share of the project.

The $300 million was also seen as a carrot to persuade MWAA to reverse its decision to offer an incentive to contractors that agreed to collective bargaining under a project labor agreement.

Many Virginia politicians disliked the airports authority’s initial support of the labor provision because they believed it ran counter to the state’s right-to-work laws and threatened to withhold financial support. The agency later changed its position slightly, offering to give contractors an incentive if they agreed to a project labor agreement, but has shown no sign of abandoning it altogether.

The prospect of the additional $300 million “raised hopes,” said Patricia Nicoson, president of the Dulles Corridor Rail Association.

But without the extra money, she said, “people feel disappointed.”

“We need additional money to support the project,” she said. “It is a question of where are we going to find it?”