Virginia, a state so strapped for road funds that it dips into the new-construction kitty to patch potholes, is about to bankroll a $1.4 billion highway.

That should be welcome news for Virginia commuters, who endure some of the worst traffic in the nation. But the project has met with blunt criticism because the four-lane highway is planned for a lightly traveled corridor.

It would run for 55miles in southeastern Virginia between Petersburg and Suffolk, parallel to U.S. 460, a four-lane road along which average volume ranges from 9,200 to 17,000 vehicles a day. The state estimates that the new highway, a toll road that would not replace the existing toll-free route, would initially carry 5,000 to 6,000 cars and trucks a day.

The traffic projections — so low that the state got no takers when it twice tried to sell the project to investors in exchange for toll revenue — have leaders from some more heavily traveled parts of the state fuming.

“It is absolutely criminal that this amount of money would be spent on a worthless road carrying 5,500 cars a day,” said Senate Minority Leader Richard L. Saslaw (D-Fairfax), noting that the Dulles Toll Road carries about 100,000 vehicles a day. “I have subdivision streets that carry more traffic than this.”

A map of the proposed toll road for Route 460

Critics can also be found in Hampton Roads, where drivers en route to Richmond or Interstate 95 could at least take the highway as an alternative to jam-prone I-64. Newport News Mayor McKinley L. Price and Portsmouth Mayor Kenneth I. Wright agree that the highway might help drivers get in and out of the congested region, but they think it would do little to alleviate traffic woes there.

“We’re still going to be sitting here in traffic trying to get around Hampton Roads,” Wright said.

The project has its champions, most notably Gov. Robert F. McDonnell (R), who has pushed for it since he was a state delegate. They largely promote the highway as an economic development project, one intended to help the state capi­tal­ize on the expansion of the Panama Canal.

Supporters say the road would spur construction of huge freight distribution centers along a corridor leading to and from the Port of Virginia in Norfolk. They say the port, with its deep channels and wide berths, could become an attractive destination for huge “post-Panamax” ships expected to start clearing the expanded canal in 2015.

“If you were to just put the blinders on and . . . look at the traffic data, you’d think, ‘Why on earth would we put $1.4 billion into a new four-lane highway there?’ ” said Dwight Farmer, executive director of the Hampton Roads Planning District Commission. “There’s a lot of growth potential, post-Panamax potential.”

Disagreement about the road is especially sharp because Virginia is in a transportation funding crisis. Since 2002, the state has been flat out of highway-maintenance money, and it has sucked $3 billion out of construction accounts to cover maintenance costs.

Finding a new source of revenue has not been easy in a tax-averse state with a flat 171 / 2-cent-a-gallon gas tax that has not brought in more revenue as the price of gas has risen.

In this year’s General Assembly session, McDonnell tried to divert some revenue from the general fund to transportation, but Democrats concerned that the plan would cheat schools and other priorities thwarted the attempt.

McDonnell has vowed to find a solution to the problem in the coming General Assembly session. Without a fix, transportation funds will be wiped out by 2017, officials say, with the new highway lapping up the last of the state’s construction dollars.

Sean T. Connaughton, the state transportation secretary, said the highway could create a new economic force in that part of the state.

“This corridor could become a major economic corridor for the state,” he said. “It’s close to the port, it runs parallel to the Norfolk Southern [railroad] main line, and on top of that, it runs right to [interstates] 95, 85 and 64. . . . We are investing a lot of money in expanding capacity in the port. We cannot send those trucks up 64 given the current problems [with that highway].”

As evidence that the highway would be important to the port, Connaughton noted that the Port Authority Board agreed to provide $250 million toward the project.

But the former board chairman said that he and others questioned the project’s value to the port and that they were removed as a result.

In July 2011, McDonnell replaced 10 of the board’s 12 members, including John G. Milliken, a former state transportation secretary who served as board chairman for 10 years. Those dismissed had been appointed by McDonnell’s Democratic predecessors and knew the Republican might replace them when their terms were up. Most were in the middle of their terms.

Milliken said McDonnell cleaned house partly to smooth the way for the highway. “Some disagreement over 460 was certainly one of the issues,” he said. In my view, that was not the best use of revenue generated by the port.”

Connaughton disputed that account. He said McDonnell made the changes because the port had been under-performing.

The new board later approved $250 million for the project. That money is being combined with $930 million in state and federal bond money. An additional $216 million is coming from the sale of bonds rated BBB-minus — just above “junk” status — and floated last week through a nonprofit public-private partnership created especially for the project.

The state also has set aside $80 million from the Virginia Transportation Infrastructure Bank as a “credit backstop” in case toll revenue is less than projected.

Virginia had hoped to get the road built at little or no expense to the state. Twice, the state put the project out to bid in recent years, hoping companies would build it in exchange for the toll revenue. But the private sector declined both times, saying traffic projections were too low to turn a profit.

The state restructured the deal before putting it out to bid a third time. Now, a private company will be paid to design and build the road. The state hopes to sign a final agreement with Ferrovial Agroman and American Infrastructure — operating as the consortium 460 Mobility Partners — in the next week. Design and right-of-way work would begin in 2013 and construction in 2014. The road would open in 2018.

Connaughton said he is aware that there are pressing transportation needs in Northern Virginia, Hampton Roads and other parts of the state. But much of what leaders are clamoring for, he said, are more-ambitious projects that the state cannot afford now.

“We have a real challenge in Hampton Roads,” he said. “You have to cross a body of water to make any sort of major steps to alleviate congestion. We examined last year the cost of building a new tunnel at the Hampton Roads Bridge-Tunnel — $5.5 billion.”

Connaughton also contends that the new highway would alleviate congestion on I-64 by providing an alternative route for vehicles traveling between Suffolk and Richmond. It would also provide another evacuation route in the event of a hurricane, he said.

The planned highway is commonly referred to as the “new 460,” though it has not been decided whether it would assume the old route number or get a new one. By whatever name, the new highway and the existing road would together carry 15,400 cars a day by 2018 and 23,000 vehicles by 2035, according to state projections that Connaughton called “very conservative.”

Critics including the Coalition for Smarter Growth and the Virginia Trucking Association contend that the projections are too optimistic, in part because trucks and cars would still have the existing toll-free route as an option. To start, tolls would be about $4 for cars and $12 for trucks traveling the entire 55 miles, officials say.

End to end, the new highway is expected to save drivers about 20 minutes compared with the old route, which has about 10 stoplights. Dale Bennett, president and chief executive of the trucking association, was skeptical that many truckers would choose to pay the premium, given the minimal time saving. Without tolls, it costs about $1.71 a mile to operate a typical 18-wheeler, Bennett said. An extra 21 cents a mile for trucks, he said, is “a significant additional operating cost.”

“Our industry operates on very thin profit margins — 2 to 3 percent,” he said. “That’s just a cost we can’t afford to absorb.”