"It could take a period of weeks or a month or two for there to be a trickle-down effect at the retail level," said Chris Galen, senior vice president of communications at the National Milk Producers Federation, a group of 30 dairy cooperatives. "What happens under this permanent law, the USDA is required to basically support a much higher price to dairy farmers."
If an agreement isn't reached, "domestic demand for dairy products would fall by an estimated 9 percent, and exports, which have seen much growth over the past decade, would likely disappear as the cost of U.S. dairy products would become prohibitively expensive," the Executive Office of the President predicted in a recent report.
In order to support these higher prices, the government would have to buy and store large quantities of dairy, which would cost "at least $12 billion per year," the report forecast.
—By CNBC's Katie Little. Follow her on Twitter