A jumble of roads and signs are seen on the Beltway looking north from Tysons Corner in this November 2012 file photo. (Dayna Smith/FOR THE WASHINGTON POST)

Gov. Robert F. McDonnell is heading into his final year in office hoping to cement his legacy as a problem solver by taking on one of the most persistent dilemmas in the state: finding a fix for roads.

McDonnell (R) is expected to unveil a proposal next week to pump at least $500 million a year into the commonwealth’s transportation coffers by 2018. Without that infusion, a state with one of the nation’s largest and most congested transportation systems will be out of road funds by 2017.

Getting his transportation package through the General Assembly in the session that begins next week would be a major coup in the eyes of supporters and burnish McDonnell’s reputation as a can-do chief executive.

But it poses political risk as well in a state weary of high tolls and the legendary traffic in Northern Virginia and Hampton Roads. Critics on the left and right are already taking shots.

What’s known about McDonnell’s package so far, they say, is a retread: McDonnell proposes taking about half of the promised $500 million from the general fund — an idea shot down by the Senate last year, saying it would cheat schools, health care and other core government services.

Virginia Gov. Bob McDonnell answers reporters’ questions after addressing a joint meeting of the House Appropriations and Senate Finance committees Dec. 17, 2012, in Richmond. McDonnell delivered his 2013 budget proposals to the committees. (Steve Helber/AP)

And no matter where the annual $500 million infusion comes from, naysayers contend it’s not nearly enough.

The battle over McDonnell’s transportation plan promises to be one of the most contentious of the session — one that could have huge consequences for both Virginia drivers and an outgoing governor with national aspirations as they head down the road.

McDonnell has not yet disclosed where the rest of the money for his plan would come from. He has hinted that he is open to linking the gas tax to inflation, but that would bring in more revenue only if the price of gas rose.

Even floating the idea of “indexing” the gas tax to inflation threatened to put McDonnell at odds with anti-tax activist Grover Norquist — an indication of just how hard it will be for a politician hoping to hang on to his conservative bona fides to find a way to pay for roads.

Still, much of McDonnell’s transportation record appeals to fiscal conservatives. He ordered an audit that turned up $1.4 billion in unspent transportation funds. He forced reforms at the high-flying board overseeing Metrorail’s $5.6 billion Silver Line.

Whatever the fate of McDonnell’s transportation package, his office contends he has done more for roads than any governor since Gerald L. Baliles, a Democrat who pushed an increase in the gas tax through the General Assembly in 1986. The tax hasn’t been raised since, and it hasn’t produced more revenue as the price of gas has risen because it is a flat, 17.5-cents-per-gallon levy.

“What Bob McDonnell has done on transportation swamps anything that’s been done by recent administrations,” said McDonnell spokesman Tucker Martin.

McDonnell accelerated bonding on projects around the state, allowing Virginia to take advantage of historically low interest rates and fire-sale pricing from contractors hungry for work amid the recession. Road projects that had long lingered in pipeline got underway: $14 billion’s worth is under construction or in the procurement process, the most in state history, according to McDonnell’s office.

“We were getting bids at like 30 percent below market, and interest rates were near zero,” said Del. David B. Albo (R-Fairfax). “He did not do anything new, but he was smart for accelerating them.”

Albo said that when it comes to road money in a state like Virginia, “it’s never enough.” But $500 million a year in new revenue would at least cover the cost of road maintenance, so the state can stop dipping into funds for new construction when it needs to make repairs.

“If he solves the maintenance shortfall, which is $500 million a year, he has achieved something that three governors previous couldn’t get done,” Albo said. “It’s a very, very big advance.”

Sen. Richard L. Saslaw (D-Fairfax) takes a dimmer view of the governor’s record. He recently spoke out against a $1.4 billion deal to build a 55-mile highway between Petersburg and Suffolk, parallel to Route 460, a relatively lightly traveled road. McDonnell has championed the highway primarily as an economic development tool that could spur development along its path.

“The last thing he will be known for is transportation,” Saslaw said. “What he will be remembered for is creating a massive debt while our roads are falling apart.”

Transportation advocates don’t dispute that McDonnell has a lot of projects underway. But they contend that he has so far failed to address the most pressing need: a long-term source of transportation funds.

“A lot of things the governor has done for transportation have merit and certainly help, but what he has said all along is, they don’t solve the problem,” said Bob Chase, president of the Northern Virginia Transportation Alliance. “The final chapter on that is yet to be written. This is the last chance to do something long-term and sustainable, and I think we all are looking forward to hearing what the governor has to say in that regard.”

Lt. Gov. Bill Bolling (R), a close ally of McDonnell’s who has become more outspoken lately as he considers an independent bid for governor, said in a recent interview that he believes the state needs about $1 billion a year in new road funds.

Chase thinks the state’s needs are higher: about $1.5 billion a year in new transportation money, $500 million of it for maintenance and $1 billion for new construction.

“It’s been more than a quarter of a century since we put more long-term money into transportation,” Chase said. “The road we’re kicking the can down has become more potholed and more congested, and the solutions have become more expensive.”