Gov. Robert F. McDonnell proposed Tuesday an ambitious overhaul of how Virginia pays for roads, rail and transit, including eliminating the gas tax and replacing it with an increase in the sales tax.

The overall plan, which would raise an estimated $3.1 billion over five years, also would increase vehicle-registration fees and add an annual $100 charge for drivers of alternative-fuel cars. McDonnell’s proposal calls for a increase in the state’s sales tax from 5 percent to 5.8 percent and projects using $1 billion in Internet sales tax revenue from legislation pending in Congress.

As he enters his last year in office, McDonnell is aiming to solve a problem that has stumped his recent predecessors: getting a tax-averse state to pay for one of the nation’s largest and most congested transportation systems — one that will run out of money by 2017.

The term-limited Republican ran for office promising not to raise taxes, but he said Tuesday that new revenue must be part of the solution. His plan also calls for devoting a greater share of existing state money to transportation.

An increase in the sales tax could be a hard sell, especially in the GOP-dominated House of Delegates, whose members are all up for reelection this year. And Democrats oppose any shifting of existing money that would affect services such as education.

Virginia Gov. Bob McDonnell, right, talks with the media at the Patrick Henry Building in Richmond, Va., Monday, Nov. 19, 2012. (Bob Brown/AP)

“We simply cannot continue to do what we have always done and expect this problem to go away,” McDonnell said. “If we stick to the old means of funding transportation, we will find ourselves having the same debates and facing the same revenue shortfalls over and over again.”

With more cars getting better mileage or using alternative fuels, he said, the flat, per-gallon gas tax no longer brings in enough money to bankroll “a safe, efficient and sustainable transportation network.”

The General Assembly is expected to take up the plan during this year’s legislative session, which begins Wednesday. If it passes, Virginia would become the first state in the country to get rid of its gas tax.

Roads are particularly congested in Northern Virginia and Hampton Roads, and planning and transportation experts have said those transportation woes threaten to stall the commonwealth’s economy.

In making his pitch, McDonnell linked his transportation plan to the state’s growth. He said that the gas tax is outdated and that although it is the largest source of maintenance funding, it does not generate enough revenue to cover the costs.

Sen. Timothy M. Kaine (D), McDonnell’s immediate predecessor, tried to solve the problem by creating regional transportation authorities to impose taxes and fees. That fix fell apart after the Virginia Supreme Court ruled in 2008 that the authorities would be unconstitutional. Before that, under then-Gov. Mark R. Warner (D), voters rejected a transportation referendum that would have levied an additional 0.5-cent sales tax on eastern and Northern Virginia to fund $5 billion in regional projects over 20 years.

McDonnell’s plan, based largely on a bill proposed by Del. Timothy D. Hugo (R-Fairfax), would maintain the 17.5-cent gas tax on diesel fuel; motorists would still have to pay the federal 18.4-cent-per-gallon levy on gas. Hugo will co-sponsor the governor’s bill in the House along with Speaker William J. Howell (R-Stafford).

Long viewed among states as a reliable source of revenue, the gas tax has brought in less money in recent years because of improved fuel efficiency and the advent of alternative-fuel vehicles. Virginia has not adjusted its gas tax for inflation in decades, leading to flat revenue, but the sales tax has continued to generate more money for state coffers. (The gas tax in Maryland and the District is 23.5 cents per gallon for regular fuel.)

Virginia is one of 27 states to tax alternative-fuel vehicles as a source of revenue for transportation improvements, according to the National Conference of State Legislatures. Several states also charge a flat fee, rather than a sales tax, to operate a vehicle powered by alternative fuels.

Some anti-tax advocates are balking at McDonnell’s measure. Grover Norquist, president of Americans for Tax Reform, said the plan “fails in its goal to prioritize transportation spending while avoiding tax increases.”

Norquist weighed in on Virginia’s transportation problem last month, warning legislators that “indexing” the gas tax to inflation — an idea McDonnell floated — would violate the anti-tax pledge they signed. On Tuesday, Norquist called for McDonnell to lower the sales tax increase, include diesel fuel in the elimination of the gas tax, nix his proposed $15 increase in vehicle-registration fees and direct more general-fund revenue toward infrastructure.

As legislators learned the details of the plan before the legislative session, which will be followed by a busy campaign season, it was unclear how politically viable the plan might be. Del. Benjamin L. Cline (R-Rockbridge), who co-chairs the legislature’s conservative caucus, said in a statement that he is ready to work with the governor but wants a “revenue-neutral” approach.

Howell was skeptical just weeks ago that lawmakers could tackle transportation this session but is now pushing the bill.

“The discussion opened up on transportation not that long ago,” he said Tuesday. “I was dubious about being able to put it together. But there’s been a lot of meetings, a lot of people meeting together, thrashing things out, and I think we’ve got a good package.” He added: “The gasoline tax, I’ve always felt was a dinosaur tax. It’s a tax that’s losing its value every year.”

But Del. Vivian E. Watts (D-Fairfax), a former state transportation secretary who attended the governor’s announcement, said the plan does not include enough money, particularly for construction. She said the state needs to pump about $1 billion a year into transportation.

“This package significantly shifts the burden of paying for our transportation needs to the backs of just Virginia residents and lets the interstate driver off the hook,” Watts said, noting that the state wouldn’t receive revenue from drivers who just fill up in the commonwealth.

McDonnell’s plan assumes $1 billion in Internet sales tax revenue over five years, contingent on federal legislation being approved. Legislation that would give states the authority to make online retailers collect sales taxes has not progressed, despite bipartisan coalitions of support on Capitol Hill and among governors. One measure, the Marketplace Fairness Act, is also backed by Amazon, Best Buy and several other major Web merchants.

“We are hopeful it’s going to go further this time,” said David French, senior vice president of government relations at the National Retail Federation, which backs the effort. One possibility, he said, is that an online sales tax measure could move this year as part of a broader tax reform effort.

Despite the criticism, Robert Puentes of the Brookings Institution called McDonnell’s plan “bold.” “The proposal to get rid of the state gasoline tax is unprecedented, that’s for sure,” he said. “It seems like it would take much longer [to get done] than the time he has left. There’s a lot to chew on.”

Mark Berman and Ben Pershing contributed to this report.