No diesel means supply chain issues for almost everything, including food.
The problems are going to start well before supplies start to run out. Trucker contracts and pay rates don't change with the price of diesel, or at least not quickly as they need to in order to respond to changes in prices.
There's a price for diesel that above which, it's no longer worth starting up a truck to pick up a load, and we're getting really close to it. At that point, existing contracts either get cancelled/abandoned, renegotiated, or completed for a net loss.
Some truckers need to stay rolling to pay their insurance/truck payment/etc... and will take routes for a loss at least for a while hoping to ride out the bad times. Larger companies will absorb losses, maybe take an insurance hit or sell off assets to keep their balance sheets green. The others? Hopefully we won't find out, but the trend would almost certainly be toward bigger companies doing horizontal and vertical integration, not toward independent truckers and owner/operators.
Those impacts wouldn't be felt as strongly in the short term, but they would be felt greatly in coming years well past the point where any corrections or changes would matter. That's far more dangerous.
My poor diesel truck is suffering.
Nor can they deliver diesel without diesel. Heating oil is a real problem too. A lot of people may freeze this winter. Even if heating fuel is available many will not be able to afford it.