House and Senate negotiators considered an entirely new transportation funding plan Monday, as they met for a second day of haggling over what could be the most important legislation of the General Assembly session.

The 10-member conference committee is trying to reconcile House and Senate bills aimed at establishing a sustainable funding source for one of the nation’s largest and most congested road systems — one on track to run out of construction funds by 2017.

Meeting for the first time Sunday, the conferees agreed that the amount raised should be about $900 million a year. That represented a concession from the House, whose plan raised between $575 million to $850 million a year, depending on the outcome of federal legislation that its bill banks on for some of the proceeds.

On Monday, the two sides began working on how to raise that money, an area of fundamental disagreement under the bills passed by the two chambers.

The House bill, based closely on Republican Gov. Robert F. McDonnell’s proposed funding overhaul, would scrap the gas tax, raise the sales tax and take $283 million a year from the general fund, which also pays for schools, public safety and other “core” government services.

The Senate version relies more on new revenue, providing just $56 million a year from existing general funds. It not only preserves the 17.5 cents per gallon gas tax but raises it 5 cents, and allows it to rise with inflation. It also imposes a 1 percent tax on the wholesale price of gasoline, and raises it to 2 percent in July 2014 if Congress does not pass a bill to allow states to collect taxes on Internet sales. And it gives localities the power to impose local sales taxes of up to 1 percent for transportation projects.

After meeting separately with the rest of the House conferees, Del. S. Chris Jones (R-Suffolk) told the full conference committee that the House still wants to eliminate the 17.5 cents per gallon retail gas tax, but it might be willing to add a 2 percent wholesale gas tax.

Jones said House conferees still want $283 million a year from the general fund to go to transportation. But he said they were open to some sort of contingency for providing the $250 million a year that would be lost if Congress does not pass the Internet sales tax legislation, known as the Marketplace Equity Act.

Jones also said they might consider supporting a plan, proposed by Senate conferees earlier in the day, to charge sales tax on car sales in lieu of the current 3 percent car titling tax. The sales tax is 5 percent but would rise to 5.8 percent under the House plan.

After Jones laid out the House’s position at the committee’s late afternoon gathering, Sen. John C. Watkins (R-Powhatan) put forward a new funding proposal.

“This is a lot simpler,” he said, as he handed out a one-page summary.

Watkins’s proposal would lower the retail gas tax from 17.5 cents per gallon to 12.5 cents per gallon, but also allow the tax to rise with inflation. His plan would impose a 3 percent tax on the wholesale price of gas. And it would raise the general sales tax from 5 percent to 5.5 percent, devoting the additional proceeds to transportation.

His plan, which would raise about $950 million a year, does not call for the transfer of any general funds to transportation. It eliminates all fee increases. (The House and Senate bills include a $15 hike in car registration fees. McDonnell also called for a $100 annual fee on hybrids and alternative-fuel cars, but both chambers nixed that.) Watkins’s plan does not count on revenue from the Marketplace Equity Act.

House members took copies of his proposal and promised to review it before meeting again Tuesday morning.