Boy this would be hard one to prove, but I am willing to take a shot at a rough estimate:
Say the DRLs consume 40 watts. Assume the average fuel to DRL conversion efficiency is 25% (and it is not this good). Assume the average person drives 12,000 miles a year and that 65% of this is at times when lights are not otherwise required. Assume the average speed is 35 mph (including highway, town, stop and go). I get the following results -
Total hours of DRL usage = 12000*.65/35 = 223 hours (could be a lot more, or somewhat less)
Energy expended by DRLs = 40*223 = 9 kwh (could be half this or twice this)
Energy consumed to power DRLs = 9 kwh/.25 = 36 kwh = 122,000 BTUs (range is probably 50,000 to 500,000)
1 gallon of gasoline = 114,000 BTUsRunning DRLs for 1 person for one year = 1.1 gallons of gasoline but the range is probably 0.1 to 10 gallons of gasoline. Given today's price of gasoline, that means drivers are probably paying from $0.30 to $30 per year to run DRLs, not including bulb replacement. So, for an individual, DRLs are not all that significant. However, there are over 200,000,000 million cars in the US. If they all had DRLs, that would mean an annual use of over 200,000,000 gallons of gasoline to keep the DRLs illuminated. That would be over a half a billion dollars.
Ed