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“We just don’t have the capacity to guarantee the construction of the garages,” Mr. York told The Times. “Having said that, we are talking with the state right now.”

In a Wednesday meeting, several members of the Loudoun County Board of Supervisors also expressed concern over paying for the garages while seeming supportive of the overall plan. The Fairfax county board will meet Tuesday to discuss Mr. LaHood’s memo.

But the decision hinges on the MWAA, since the board is responsible for overseeing the entire extension project.

“I hope MWAA will start taking this stuff seriously and understand why the funding partners are where they are and understand the aerial station is not inconvenient to passengers,” said Mr. York, an independent. “Most importantly, Loudoun and Fairfax County are not cash cows for MWAA.”