Northern Virginia liberals have already lost two rounds in the multi-year bout over building Metrorail’s Silver Line to Dulles Airport and Loudoun County. Now they should prepare for a third setback, as a price of getting conservatives’ support to complete the invaluable project.

Liberal transit advocates lost in 2006 when they grudgingly gave up on digging a full four miles of rail tunnel under Tysons Corner in Fairfax. Instead, to reduce costs, they had to settle for just a half-mile underground. The remaining 3 1 / 2 miles will be perched on intrusive elevated tracks.

They succumbed again last year by agreeing to an above-ground station at the airport. It was less convenient but, again, less expensive than their preferred underground alternative.

Now the liberals are likely to have to yield in an arcane, partly symbolic dispute over the role of labor unions in building the tracks and stations.

Republican leaders in Richmond and Loudoun are threatening to slow or even block the $2.7 billion second phase of the Silver Line unless the construction plan is modified to kill a pro-union preference.

With Republicans controlling the governor’s mansion, the House of Delegates and the Loudoun Board of Supervisors, they almost certainly have the clout to prevail.

The GOP also has history on its side. The unions are the ones trying to change the ground rules, albeit subtly, by adding a provision that wasn’t present for the first half of the project.

“Labor is trying to win politically what they can’t win in the marketplace,” a senior Northern Virginia transportation official said. Like other sources for this column, the official spoke on the condition of anonymity to avoid offending others in the negotiations.

Some influential local Democrats, notably Fairfax Board of Supervisors Chairman Sharon S. Bulova, have already adjusted to the prevailing wind. Last month Bulova joined two top Republicans — Virginia Transportation Secretary Sean T. Connaughton and Loudoun Supervisors Chairman Scott K. York — in urging the agency overseeing the rail project to drop the pro-union provision.

Extending the rail line to Dulles and beyond is vital to the region. It would link our principal international airport to the rail transit network. It would foster smart growth and reduce highway congestion in affluent, fast-growing communities.

In practical terms, the stakes in the union dispute are surprisingly modest. The argument has nothing to do with the construction workers’ wages and benefits, which are fixed by federal law.

Instead, the fight is about whether to formally encourage adoption of pro-union work rules during construction. The provision targeted by the GOP says companies that agree to a pro-union Project Labor Agreement, or PLA, would receive a 10 percent bonus when their bids for the lucrative contract are evaluated.

A contractor using a PLA would have to find workers through union hiring halls. It would have to hire extra people for certain tasks.

The Metropolitan Washington Airports Authority, which is overseeing the Silver Line’s construction, adopted the pro-union preference in February. Most of the authority’s board members were appointed by Democrats.

Ironically, despite the GOP’s concerns, many big contractors are perfectly happy using PLAs. The pacts add cost — from 3 percent to 20 percent, depending on whom you ask — but also make it easier to find qualified workers and to prevent strikes.

Dulles Transit Partners, the prime contractor for Phase 1, voluntarily adopted a PLA. There’s a good chance that the winning contractor for Phase 2 will use a PLA regardless of whether the bidding process includes a preference.

“Getting labor peace for a couple of years, that might not be a bad thing,” said a Republican lawyer familiar with the local construction industry.

Given all that, why is the GOP so determined to kill the PLA provision? It’s mostly about anti-union ideology. The airports authority hasn’t used formal, pro-PLA preferences before. Conservatives are worried the precedent would weaken Virginia’s status as a right-to-work state.

There might be a silver lining for Democrats. In the current budget negotiations in Richmond, Senate Democrats have succeeded in putting on the table a proposal to raise the state’s contribution to the Silver Line project from $150 million to $450 million.

The Republican-dominated House isn’t enthusiastic about such spending. So this creates a potential, natural compromise.

The Democrats’ share of the bargain would be the extra $300 million, which would go to help hold down toll increases on the Dulles Toll Road. In return, the Republicans would win elimination of the PLA preference.

“If you think anti-PLA language is worth $300 million, my position is, sure, you can have it. You’re going to end up with a PLA anyway,” said a state legislator who represents a Fairfax constituency.

No matter how much posturing and maneuvering it takes, the most important thing is: Get the project done.