It's the Huffington Post, so read into it what you will. Like I said, I don't know much about the Dairy portion of the farm bill.
If the negotiators can't agree on a bill and Congress allows the dairy supports to expire, 1930s and 1940s-era "permanent" farm law would go into effect. Those laws would raise the price that the government currently pays to purchase dairy products, prompting many processors to sell to the government instead of commercial markets. That would decrease commercial supply and consequently raise prices for shoppers at grocery stores.
Prices wouldn't go up immediately, as the Agriculture Department would have to write the new rules based on the old laws and then put them into place. But Agriculture Secretary Tom Vilsack is warning that it may not take that long, saying USDA was prepared to implement the dairy law in "short order" if current law expires.
That seems like hokey math to me, unless the government is willing to buy unlimited supplies of the milk at the higher price, it sounds like it's getting quite overblown.