RICHMOND — Virginia House and Senate conferees struck a deal Wednesday to overhaul transportation funding in a state set to run out of construction funds by 2017.

“We have a deal on transportation!” Sen. John C. Watkins (R-Powhatan) said in a blast email shortly after the conference committee broke up for the morning. “Details to follow.”

The plan will still have to pass muster with the House and Senate, whose members were expected to be briefed on the plan Wednesday morning.

Details of the plan were not yet clear. But the 10-member committee moved closer to a transportation-funding deal late Tuesday that would substantially cut the fuels tax but raise the sales tax from 5.0 to 5.3 percent, and divert a portion of existing revenues to roads.

As part of the Tuesday night offer, the GOP-led House said it would remove the 17.5 cents-per-gallon gas tax but impose a 3.5 percent wholesale gas tax.

The House negotiators also offered to reduce the amount of general fund revenues that Gov. Robert F. McDonnell (R) and the full House had sought to use for roads. But the new offer would still be more than the amount agreed to so far by the Senate. The House’s offer also would earmark more of the new sales tax revenues to education.

Senate negotiators planned to consider the House offer overnight.

As of Tuesday night, one major difference in how much of the general fund, which is derived from income and sales taxes and pays for schools, law enforcement and many other services, should be used on transportation.

“We’re slowly getting there,” said Sen. Frank W. Wagner (R-Virginia Beach) told Del. S. Chris Jones (R-Suffolk) after Jones laid out the House’s second counter offer Tuesday. “I’m encouraged.”

Del. David Albo (R-Fairfax) said the House offer was faithful to the governor’s attempt to replace the gas tax – whose revenues have drastically diminished because of inflation and increased fuel efficiency in vehicles – with a source of funding that will grow as the economy and tax receipts grow.

“We feel like we implemented the governor’s basic thesis, which was to tie transportation to something that grows,” Albo said. “It’s much different from the governor’s original bill, but I think it hits his basic thesis.”

But Sen. Janet D. Howell (D-Fairfax) expressed some doubt about whether such a plan would fly in their respective chambers.

“We’re [in] a better position than we were when we started,” she said. “Are we far enough to get votes? I don’t know that.”

The House proposal would leave the diesel fuel tax essentially unchanged, though it would be converted from a per-gallon levy to 6 percent wholesale tax so that it would rise with inflation. There would be a $100 fee on alternative fuel vehicles – a key proposal by the governor to ensure that vehicles that that pay little for gasoline still contribute toward maintaining roads. Titling fees for car purchases would also rise. Now 2 percentage points below the sales tax, it would change to 1 percentage point below.

The House also offered a local-funding mechanism to be enacted by the legislature that would raise additional funds in those traffic-congested areas, such as Hampton Roads and Northern Virginia, and dedicate those funds for use only in those localities. The latest offer would generate as much as $350 million a year for Northern Virginia and perhaps as much as $200 million for Hampton Roads. Albo said the bill would even contain “kill switches” that mean the higher taxes would be removed if the revenues were used for purposes other than transportation or diverted from the areas where they were raised.

The proposed compromise would use about $200 million a year in general fund revenues once the plan is fully implemented, compared with McDonnell’s target of $283 million. The Senate bill called for $56 million a year from the general fund.

Del. Onzlee Ware (D-Roanoke City), who is on the panel, said Democrats remain wary of using too much money from the general fund because it could starve other programs.

“I appreciate some movement away from the $283 million,” he said.

Albo said that on balance, between tax increases and cuts, most Virginians would break even under the latest proposal.

“We think the average citizen is going to break even,” he said. “The reason the plan works is it grows over time. The trucker’s going to pay more.”

The new proposal would raise approximately $869 million a year when fully implemented. That’s less than the Senate’s desired $952 million, and below the $900 million that House and Senate conferees agreed would be their target as negotiations got underway Sunday.

“If we continue to make the progress that we’ve made so far, we’ll have a conference report that will have the required votes to pass the Senate and the House,” Jones said.

The conference committee will meet again at 8:30 a.m. Wednesday.