After years of strife between dockworkers and terminal operators at West Coast ports, both sides in ongoing contract negotiations are taking a decidedly more positive tone in the talks, providing hope that a work stoppage can be avoided when the contract between union dockworkers and terminal operators ends at 5 p.m. Pacific Time on Tuesday.
"Negotiations will continue on Monday and likely to continue into mid-July," a spokesman for the Pacific Maritime Association, which represents port employers, told CNBC,
The International Longshore and Warehouse Union struck a similar tone, saying that both sides plan to be back at the bargaining table Monday afternoon local time.
Read MoreHope you owned these 11 stocks this quarter
In 2002, a 10-day work stoppage on the West Coast ended only after President George W. Bush invoked the Taft Hartley Act, forcing port operations to resume.
According to the U.S. Census Bureau, West Coast ports handled $892 billion worth of cargo in 2013 alone. A study commissioned by the National Retail Federation and the National Association of Manufacturers claims that if no agreement is reached, it could cost the U.S. economy up to $2.5 billion a day.
Operators at 29 ports are negotiating a new contract with about 20,000 port workers, including labor at the ports of Los Angeles and Long Beach, the two biggest container ports in the nation.
Bill Allen, president and CEO of the Los Angeles Economic Development Corporation, told CNBC that the region cannot afford a string of closed ports from Seattle to San Diego.
—By CNBC's Paul McNamara