A sustained and significant rise in oil prices could derail the U.S. economic recovery by stirring inflation and putting the brakes on spending.

Oil futures touched $100 a barrel at the New York Mercantile Exchange Wednesday—the highest since before the financial crisis hit in late 2008—before pulling back. Pricier oil drives up the costs of everything from gas at the pump to the raw materials used to make nylon and food packaging. That could mean higher inflation and prompt...