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Mr. McDonnell said his proposal will “make a game-changing investment” in the state’s transportation system. Because state law gives highway maintenance priority for gas tax revenues, very little money has been available in recent years for new construction.

“Instead of building new roads, we’re doing paving and potholes,” he said, adding that his plan would end that problem by 2019.

House Speaker William J. Howell, Stafford Republican, called Mr. McDonnell’s plan bold and said he has long considered the gas tax “a dinosaur.” Mr. Howell; Delegate Tim Hugo, Fairfax Republican; and Sen. Stephen D. Newman, Lynchburg Republican, are sponsoring the legislation.

Delegate Vivian E. Watts, Fairfax Democrat and a former state secretary of transportation, said she was “not impressed” with Mr. McDonnell’s final effort to do something on transportation before his nonrenewable four-year term ends next January.

“It’s not nearly enough money,” she said. It also puts too much emphasis on highway maintenance, lets out-of-state motorists drive on Virginia’s highways without paying their fair share and does not do enough for the heavily congested “urban crescent” from the D.C. suburbs, through Richmond to Hampton Roads.

Americans for Tax Reform, the conservative organization headed by Grover Norquist, also criticized the proposal.

The group said in a statement, “The plan as it stands now fails in its goal to prioritize transportation spending while avoiding tax increases.”