One of the most powerful conservative groups in the country is bankrolling robo-calls in a sliver of Northern Virginia. But the calls aren’t rallying the opposition to President Obama.

Instead, Americans for Prosperity is jumping into one of the Washington region’s most heated issues: the planned multibillion-dollar extension of Metrorail from Reston to Dulles International Airport and into Loudoun County.

In thousands of phone calls, it is urging residents to tell local elected officials that they oppose any tax increases to pay for the new Silver Line.

“Loudoun cannot afford this bail-out to rail-station developers,’’ according to a script of the call. “If the Loudoun County board opts out, the rail will still be built to Dulles Airport, and commuters will still be within five miles of Metro. Come tell the board of supervisors to opt out and save taxpayers billions of dollars.”

Americans for Prosperity, a group founded with support from the billionaire Koch brothers, advocates lower taxes and smaller government and has long involved itself in tax issues in Virginia and across the nation. The organization, which has its national headquarters in Arlington County and a state chapter in Richmond, played a significant role in the Republican takeover of the U.S. House in 2010 and has aired $7 million in anti-Obama TV ads during this election cycle.

Those in favor of the project have been lobbying, too — circulating petitions at park-and-ride locations and hiring lobbyists to contact the Loudoun County Board of Supervisors. Labor organizations have taken out full-page ads in a local paper.

“This is a big deal to Loudoun County,” said Tony Howard, president of the Loudoun Chamber of Commerce, which supports the project and is lobbying board members. “There are folks with passionate opinions on both sides.”

Audrey Jackson, state director of Americans for Prosperity-Virginia, said her group began calling thousands of residents — supporters, tea party activists and likely conservative voters — to oppose the “major tax increases” needed to fund the second phase of the Metrorail extension.

Loudoun supervisors will meet Monday to hear residents’ comments about the Silver Line. Already, more than 100 people have signed up to speak. Americans for Prosperity is planning a rally outside the government center that night.

Supervisors will meet again Wednesday to discuss possible options for financing the project. Those include the establishment of a countywide commercial and industrial transportation tax – similar to those used in Fairfax and Arlington counties – or the creation of a special tax district encompassing areas closest to the Silver Line.

Supervisor Matthew F. Letourneau (R-Dulles) said the county does not necessarily have to increases taxes to pay for the project.

“At the end of the day, five of us have to decide that this is a project worth doing as a county,’’ he said. “And if we believe that, then we can find a way to make it work without really impacting the tax rate.”

Jack Potter, chief executive of the Metropolitan Washington Airports Authority, said that he is “pro-rail to Loudoun’’ but that ultimately the decision on whether to participate has to be made by Loudoun.

If Loudoun backs out, he said, designs would have to be reworked to deal with parking at the last stop, at Dulles Airport.

Next week, the airports authority, which is overseeing construction of the $6 billion Silver Line, is expected to vote on whether to press ahead with a controversial project labor agreement.

Loudoun supervisors have said they are reluctant to fulfill the county’s $200 million commitment to the project if the union-friendly agreement for contractors remains. Loudoun has until July 4 to decide whether it is in or out of the project.

Virginia Gov. Robert F. McDonnell (R) has said the state will withhold its $150 million contribution to the planned Metrorail extension unless the labor agreement is dropped.

The first phase of the Silver Line is under construction from Falls Church to Reston and is scheduled to be completed in late 2013. Construction on the second phase, which would run to Dulles and into Loudoun County, is expected to start early next year.

Staff writers Caitlin Gibson and Dana Hedgpeth contributed to this report.