The challenges with such a shift are immense. Economists are not sure the idea will be practical, and privacy advocates oppose the notion of governments monitoring motorists’ driving habits. But millions of dollars are being spent on experiments with ways to collect such fees, and the idea seems to be gaining support in some quarters.

“We’re anticipating that we may get to the day when cars on the road don’t ever even go to a fueling station,” said Representative Peter A. DeFazio, an Oregon Democrat and chairman of the House Subcommittee on Highways and Transit, which held hearings on the matter last summer. “If we’re going to continue to have a highway network and fix the 150,000 bridges we have that are in disrepair, we’re going to need new sources of revenue.”

Gas tax revenue has been flat or declining across the nation, partly because people are driving less and partly because their cars require less fuel. The Department of Transportation took in about $71 million less in gas taxes in the 2008 fiscal year than in 2007, and Americans drove 12.9 billion fewer miles in November 2008 than November 2007, the most recent figures available.

Those declines have depleted the Federal Highway Trust Fund, authorized by Congress in 2005 to pay for road construction and maintenance through the end of this year. The federal tax rate of 18.4 cents per gallon of gas has not changed since 1993; 24 states and the District of Columbia have not changed their per-gallon tax rates since 1998.

The matter bubbled up at the White House recently after President Obama’s transportation secretary, Ray LaHood, said the administration was considering some form of a “vehicles miles traveled” tax to replace the federal fuel tax. Mr. Obama’s press secretary, Robert Gibbs, corrected Mr. LaHood, telling reporters at his daily briefing the next day that supporting such a tax “is not and will not be the policy of the Obama administration.”

Still, studies of variations of a mileage tax are being conducted. In the largest experiment of its type, the $16.5 million federal Road User Study, more than 1,200 volunteers in six cities are driving cars equipped with tracking devices to record where motorists have been. The drivers pay the traditional gas tax when they fill up, but they also receive simulated bills each month based on mileage, showing how such a system may work.

“We’re looking at how you would bill people, at invasion of privacy issues, and, human nature being what it is, people will always be looking at ways to beat the system,” said Jon Kuhl, principal investigator for the Road User Study, which is using volunteers in Austin, Tex.; Baltimore; Boise, Idaho; Raleigh and Durham, N.C.; San Diego; and the Quad Cities region of Iowa.

In a $2.7 million field test that ended in 2007, Oregon officials equipped the cars of 299 volunteers with transponders that relayed mileage data to special gas pumps. The pump charged the drivers 1.2 cents per mile in lieu of the 24-cent per gallon state gas tax. Gov. Theodore R. Kulongoski, a Democrat, has asked the Legislature to approve $10 million to refine the technology and conduct more field tests.

Others are also tinkering with the idea. The North Carolina Legislature is considering adding a fee of one-quarter of a cent per mile to the state’s current tax of 30.2 cents per gallon. The mileage fee would be paid with the annual vehicle registration fee.

In Massachusetts, Gov. Deval Patrick, a Democrat, is considering a similar fee that would replace the gas tax. The Nevada Transportation Department is spending $200,000 on a study before deciding whether to ask the Legislature to authorize a trial in 2011 in which some motorists would be charged a mileage tax instead of the gas tax.

Nevada plans to study the feasibility of charging motorists more for driving on the interstate during rush hour than on a surface street at midnight as a way to encourage alternative routes and carpooling. Mr. Kuhl of the Road User Study and other supporters of a mileage tax contend that motorists in many regions, including the New York metropolitan area, may buy their gas in one state but do much of their driving in another.

“We’re seeing more fuel-efficient cars or even cars that run on electricity,” said Susan Martinovich, director of the Nevada Department of Transportation. “Those people are not paying as much, and yet they’re still on the road and still causing congestion and impacting pavement. How do I get at those people?”

Privacy advocates and economists, though, wonder about the complexity — and the public’s reaction to tracking where and when people drive.

“You’d have to have a record where the car is at all times, and that certainly would frighten America,” said Mike Moffatt, an economist at the Ivy School of Business at the University of Western Ontario. “And it also seems like a much more expensive way to collect taxes.”

Despite the problems, some move to replace or supplement the gas tax seems inevitable. Mr. Kuhl envisions retrofitting vehicles with a transponder to measure miles traveled, but Jim Whitty, the Oregon transportation official who oversaw the 2007 pilot program, said it was more practical to require automakers to install them in new cars and start the switch with those owners.