I Disagree!!!!
However, it would take someone a long time to try and work out the figures, there would be some approximations made, and, hence the final figure would not be totally accurate. But I believe it should be possible to get it fairly close. . .
Eg for the manufacture of the furnace, say, the total carbon footprint of it's manufacture
should be calcuable (mining, smelting, transport, retailing etc). Let's say 100kg of carbon (Still not sure if that is Carbon released into the atmosphere, or CO2 btw!!

). But in the lifetime of the domestic furnace (say 30 years, burning 2 tonnes of coal a year, 100kg is a very small percentage of 60,000 kg (30*2000kg), so negligible and we can ignore it (!) (ok, about 0.2% then)
For a car, I'd imagine the carbon footprint of the total manufacture would be a lot higher, eg 2 tonnes of carbon in total. Life of car = 100,000 miles. 40mpg, say 10 miles per litre, say 1 litre of fuel weighs 0.8 kg, that's 10,000 litres at 0.8 kg per litre, ie 8 tonnes of C released in the lifetime of the car (double that as the carbon footprint websites indicate it is more per mile).
In this case, the manufacture of the car would come out as something roughly like 12.5% that of the fuel used to power the car.
ie NOT negligible
I'm sure the figures for fuel aquisition and refining ,transport, transport and retail are out there too . . . . . somewhere! (Or we could try and work them out, let's see, hmmm, maybe not right now . . . :eek!: )
(Apologies if my figures are approx, no prizes for spotting any errors, like in the order of magnitude range for example . .)