RICHMOND — What do a Democratic senator from northern Virginia and a Republican presidential candidate have in common?

Both want to eliminate Virginia’s unpopular car tax.

Sen. J. Chapman Petersen (D-Fairfax) filed bills on Monday that would do away with the fee, which also happens to be a signature issue of former governor James S. Gilmore III.

Gilmore, who is in the back of a crowded field of White House hopefuls, ran for governor in 1997 on a “No Car Tax!” pledge, but was never entirely successful.

“I just think the public is very frustrated they have to continue to pay it,” he said in a phone interview Monday. “It’s not good. We should have just gotten rid of it altogether.”

The car tax, which was at the heart of then-Gov. Mark Warner’s legendary 2004 budget deal, has long roiled Virginia politicians who have searched for a way to do away with it without leaving counties and cities in the lurch.

“The time has come to finally get rid of the car tax once and for all,” Petersen said. “It’s been hanging out there for years, it’s kind of half in, half out.”

Petersen proposes first eliminating the tax through a constitutional amendment and then giving localities the option of levying a gas tax to make up for the lost revenue.

The car tax punishes law-abiding drivers who register their cars in the state, bills them in one lump sum and is an administrative nightmare for localities that have to factor in a state reimbursement, Petersen said.

“The whole thing is sort of a mess in my opinion,” he said.

Support for killing the tax got a boost about a year ago when Gilmore hoisted an ax above his head during a speech at a Republican retreat and started a chant of “Ax the tax!”

[Dec. 2014: Gilmore raises national profile, won’t rule out presidential bid]

Rather than Petersen’s approach of replacing one tax with another, Gilmore said he wished he could have found away to repeal it fully when he was governor.

He ran on a promise to eliminate the personal property tax that cities and counties across the state levy on automobiles. But because localities relied heavily on that revenue to fund services, the state felt the need to reimburse them.

The cost to the state was expected to be about $600 million, but with cars growing more numerous and expensive, the tab kept climbing. In 2004, under Warner (D), the state capped it at $950 million a year.

At the time, supporters said the tax break, which is applied to the first $20,000 of a car’s assessed value, provides much-needed financial relief to ordinary families who need vehicles to get to and from work.

Critics consider it a shell game because taxpayers ultimately are still footing the bill through the state levies that fund reimbursements to the localities.