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But Mr. Snelling — and a majority of the COG board — disagreed.

“Combined with the extra four directors, the net effect would be to transfer absolute control of the airports to Richmond,” Mr. Snelling said. “We have great concerns since the airports themselves are federally owned and regional assets that serve passengers from throughout the metropolitan area.”

Despite the opposition lodged Wednesday, the Quinnipiac poll shows that Mr. McDonnell scores well with a broad range of voter blocs.

Independents favored him by 65 percent to 18 percent, while Democrats were split at 40 percent who approved and disapproved of his job performance.

And while his lowest marks came in Northern Virginia, lately a Democratic stronghold, 60 percent of voters there said they approved of the governor’s job performance.

“When people look at Gov. McDonnell, their evaluation is more on whether they like him and how they feel the economy’s doing in Virginia, rather than the intramural struggles of who gets to sit on the Metro Board,” Mr. Farnsworth said.