I read the title thinking you meant gas (i.e. the mostly methane stuff we use over here for central heating and if you have a gas cooker). I was going to suggest that people could manage just fine with electric heaters even though they're a total pain, albeit if you had a gas cooker you'd have to buy an electric one if there's a long term gas shortage. lol.
But upon reading the question, you meant petrol. Okay I don't have experience of a petrol shortage, but I do know how quickly everything shuts down because people can't drive to work - a la the "Beast from the East" snowstorm in March (yeah, British weather never bothered itself about seasons) where the local council ran out of grit after a few hours and the roads became like a giant ice rink. No-one could drive anywhere so everyone had to stay at home. It didn't matter because it was only for a couple of days, because our totally irrational weather caused the ice to have all melted by Saturday afternoon. But what you're talking about is a long term situation where no-one can drive to work. And the USA is a lot more dependent on cars than the UK. But why aren't we so dependent on cars? We have good public transport... but buses need petrol, albeit trains run on electricity. But what are they putting in the power stations to make the trains run? In the Beast from the East, the entire local bus company stopped running, loads of trains were cancelled (and people were stuck overnight on trains that were stranded mid-journey as the tracks became impassable). The entire transportation system - roads and rail - shut down. No-one could go anywhere.
What happens to an economy when no-one can get to work? A few people would be able to walk to work, but probably not enough people to keep the various businesses running. If the various businesses and services can't keep running, well, there won't be those businesses and services any more.
During Beast from the East, lots of people with 4x4s banded together (organising themselves online) working with emergency services to drive emergency service workers to work if they were unable to get in, so the hospitals and emergency services could remain running. However, while 4x4s are good in a snowstorm, they still run off petrol (rather a lot of it at that), so even emergency services would shut down. Plus, ambulances, police cars and fire engines need petrol.
Diesel cars can be converted to run off chip fat. I mean vegetable oil. The stuff you deep fry chips in. By chips I mean fries. I'm assuming that if there's no petrol there'd be no diesel either, but those who do have a diesel car, if they know a mechanic who knows how to do the conversion, they could run their cars off chip fat. That would alleviate some of the problems.
Also, if there's no petrol, there'd be no other hydrocarbon fossil fuels like diesel or kerosene (jet fuel). Petrol is octane, i.e. the hydrocarbons with 8 carbons but it's made by fractional distillation from crude oil, and the other things like diesel, kerosene, and gases like methane, are just hydrocarbons with different numbers of carbon atoms. So I'm assuming that no petrol is the result of no crude oil, therefore there'd be none of the other products of fractional distillation. What's going into the power stations? No-one would have electricity if it's all currently coming from products of crude oil. How much of the electricity comes from green sources, or other sources that don't require crude oil? No electricity = even worse problems. But people may be able to power their homes through microgeneration (e.g. your own personal solar panel or wind turbine). Some companies may have their own generators (though if they run off fossil fuels they won't work any more). But if no-one can get to work in the first place, microgeneration isn't going to solve anything.