The good news: 2014 was a fantastic year at the nation's largest container port complex in Los Angeles and Long Beach. Volumes rose 4 percent to the highest level since before the recession, a sure sign of a rebounding economy. The bad news: There's a lot of cargo stacked up at the docks going nowhere. And the gridlock seems to mirror the lack of progress in contract talks between terminal operators and longshoremen.

Disruptions are costing meat and poultry producers $30 million a week in losses, according to the North American Meat Institute. The president of the Footwear Distributors and Retailers of America said this is a critical time for the industry, and a potential full stoppage at the ports would be "catastrophic." UPS on Thursday attributed an expected fourth-quarter profit shortfall to the port slowdown.

"This is literally an international incident," said John Demshki of CCH Citrus, one of the nation's largest citrus exporters. Delays are costing him sales to China, where California navel oranges are popular for the Chinese New Year. Read MoreUPS shares fall on lower fourth-quarter guidance Management and labor at the ports are blaming each other for the epic congestion. And it appears impossible for both sides' stories to be true. "Those problems have been created by mismanagement of the terminals," said Bobby Olvera Jr., president of ILWU Local 13, representing longshoremen. He said management—the Pacific Maritime Association, or PMA—is intentionally asking for only half the normal labor to move cargo and then publicly blaming the union for the slowdown. "We had over 1,000 members checked in to work last night," he said earlier this week, "and the employer ordered 200 jobs."

Cranes for unloading shipping containers stand at the Port of Los Angeles in San Pedro, California. Patrick T. Fallon | Bloomberg | Getty Images

Not true, said Tony Scioscia, a former PMA board member who now has a shipping consulting business. Scioscia said management is asking for a full contingent of dockworkers, but the union is not providing enough workers. "The terminals, since early November, have been operating with about 50 percent of the people they need," he said. Who is telling the truth? It's not clear. In the middle are dispatchers, joint employees of the union and terminal operators. Dispatchers take calls from operators ordering a certain number of "gangs" to work ships and then put out the call in halls where workers are gathered. For example, a large ship might need six gangs. Longshoremen claim management will currently ask for only three gangs, slowing things down. The PMA claims it's asking for six gangs, but longshoremen will only offer up three. When it was pointed out to Scioscia that both sides can't be right, he replied, "You're absolutely accurate." CNBC has an ongoing effort to get inside a dispatch hall to gauge the situation first-hand. Read MoreBaker Hughes to lay off 7,000 workers, sees downturn Congestion was building for months even before the slowdown, due to issues unrelated to the contract dispute. Larger ships have been bringing in more cargo, and there's an ongoing shortage of functioning trailers to hitch containers to trucks. The environment is miserable for John Demshki, the citrus grower. "Normally a voyage to your customers would take 18 to 22 days," he said. "We're having some customers getting their fruit 40 to 45 days after we've actually processed the fruit. The problem with that is our fruit is perishable." As a result, Demshki has slowed harvesting to keep fruit on trees longer. Shipping through Texas or Mexico isn't worth the extra cost…yet. "I have my trading partners now buying Turkish lemons when they've never handled a Turkish lemon. We have Spanish lemons going into our competing marketplace where we outmaneuvered them and out-qualitied them many years ago." (On the flip side, this could be good news for American consumers, as the slowdown in exports could create an oversupply at home, which would drive down prices.) Adding to the slowdown, the PMA has ordered a stoppage on most work unloading ships at night in Los Angeles and Long Beach until more space clears up for containers. The longshoremen claim two terminal operators have defied the PMA and worked at night, resulting in fines of $50,000 and suspension from the PMA. The PMA will not comment, and calls to the terminal operators involved were not returned.

At the end of the day, the goal isn't to warehouse containers. It's to keep them moving. Steve Getzug spokesman, PMA