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And he privately put the arm on individual lawmakers he summoned to his office.

By Tuesday, a well-choreographed round of emails from House GOP leaders and a few business groups carefully and broadly endorsing his proposal went out to distribution lists that included Virginia’s Capitol press corps.

But the statements masked a number of concerns that have to be resolved over the 34 remaining days of the 2013 General Assembly session.

Lt. Gov. Bill Bolling, spurned by the state GOP in his quest for its gubernatorial nomination and sporting a newfound independent streak, counts himself a supporter of Mr. McDonnell’s plan right now but says it needs work. Mr. Bolling’s personal preference is to revise the gasoline tax, something with a direct tie to highway usage and what he calls “the ultimate user fee.”

“I think the governor believes this bill gives us the best chance we need to pass a transportation bill in the Senate and in the House of Delegates, but I think the governor is open to other ideas,” he said Friday. “It depends on what those ideas are.”

How far will he go?

The governor’s policy team, thirsty for a major victory, says Mr. McDonnell is open to redecorating the room, but not to knocking out the walls and drawing new blueprints. That means the sales tax increase will have to be its centerpiece.