We already know how to create biodiesel and other fuels from non fossil sources. If we limited their use to critical needs, and had everything else using renewable electric sources, then we probably could do without oil.
The problem is that we don't just use fossil fuels for fueling our cars and power pants. It makes the polymers used in almost every electrical component. It fuels the industrial mining of almost every metal and mineral used in those components (good luck hand-panning for rare earth minerals, or removing millions of tons of earth using only steam engines). It fuels the entire shipping industry that moves everything around (enabling modern industrial processing of raw materials).
Oil and coal do a fuckload lot more these days than make gasoline for our little cars and run our power plants. That's just the obvious use that most of us see every day. Odds are that every single thing your own today is either made from petrochemicals or somehow heavily dependent on them. I myself own exactly one piece of wood furniture made by a local artisan and a few books left by my great-grandmother that may be exceptions to this. Everything else was shipped using petrol, created with coal-based power, or contains petrochemical based polymers. Even the food I eat is mostly shipped in from large farms and ranches in another part of the country.