Can the problem causing the rotten egg smell from my car also be the cause of the loss of gas mileage?

You have an overly rich air/fuel mixture ( below 10 parts air to 1 part fuel) causing a sulfur smell and high fuel consumption. A normal air /fuel mixture is ideally 14.7:1. You need to look for what is causing the over rich mixture. Many things could contribute to this condition,some are: high MAP sensor voltage signal caused by a vacuum leak or electrical problem, leaking fuel injectors, high fuel pressure, leaking fuel pressure regulator, engine not getting hot enough,oxygen sensor sending a weak voltage signal back to the computer causing the computer to correct the fuel trim to a false lean condition, faulty coolant temperature, false signals from the mass air flow meter, problems with the EVAP emissions system and so on... The first place to start is scan the cars on-board computer and retrieve any diagnostic trouble codes and fix them first. If an over rich air/fuel mixture is let go too long it can cause your catalytic converter(s) to melt down thus restricting the exhaust resulting in an un-driveable car due to extremely poor acceleration (and a very high priced repair). If the "CHECK ENGINE" light is blinking as you drive that is a true indicator that the mixture is rich and damage to the converter(s) can result. Car makers built this feature into OBD II systems to warn drivers of the pending catalyst damage. In that case I would recommend that you have the problem fixed right away or it could end up costing a bundle if you wait.

Almost all the above answers are almost correct. By design, the catalytic converter converts the exhaust byproducts into hydrogen sulfide and water. Sometimes this mixture is a little off balance and creates sulfuric acid which is only one molecule away but that doesn't happen all that often. Sulpher is the chief byproduct of rotten eggs which is why the smell. Under ideal conditions the converter would not produce enough sulpher to cause the strong smell but it almost always produces a mild smell and you just don't notice it. Have you ever been driving and smell the sulpher when cars pass you? Don't be concerned about the smell unless it's just so strong you can't stand it. As you put some more miles on your car, the smell will lessen as the catalytic converter "wears out" some.

Odd you don't mention the check engine light is on. Yes, the rotten egg smell is the result of the mixture being too rich. When the mixture is correct or lean the converter can oxidize the sulfur in the fuel to sulfur dioxide - nasty in its own way but at least not stinky. When the mixture is too rich the converter steals some oxygen from the water vapor that makes up a large part of the exhaust and combines the leftover hydrogen with the sulfur to form hydrogen sulfide - the rotten egg odor. The rich mixture also means you are using more fuel than you should be - lower fuel economy. The rich mixture can also damage the catalytic converter so don't put it off.

The rotten egg smell is from too much unburned fuel getting to the cat . Could be a bad mass airflow sensor or a plugged intake like an air filter being dirty . Maybe a good tune up would be a good place to start . I would get it fixed before it does damage the cat .

this happened to my moms car for her the fix was a vacuum line not hooked up. causing to much gas not getting burned and settling in the cat converter. stinks!

that,s the cat, that,s clogged up and yes it can cut down on gas mileage and also loss of power too.

Sounds like catalytic converter is bad.

I would imagine so lol