A federal mediator was unable to broker an agreement after meeting with both sides Tuesday, said Gary Quick, the chairman of the union's negotiating committee.
"We're out picketing now" at the company's Huntington Beach plant, he said.
Boeing spokesman Dan Beck said the company's offer would have given workers "substantial" pay increases and boosted pensions and savings plans.
"Boeing still stands by the fact that we feel we gave a very excellent offer," he said.
The strike could affect satellite launch facilities operated by Boeing's Integrated Defense Systems unit at Vandenberg Air Force Base in California and Cape Canaveral in Florida.
Already, the launch of one Delta rocket carrying NASA environmental satellites was delayed at Vandenberg because of the strike threat.
Two weeks ago, locals with the International Association of Machinists and Aerospace Workers in California, Alabama and Florida, rejected Boeing's latest offer for a three-year contract.
The current three-year contract expired Oct. 23. It covers about 900 workers in Huntington Beach, Torrance, Vandenberg and Edwards Air Force Base in California; about 300 workers at Cape Canaveral in Florida; and about 300 workers at Boeing facilities in Huntsville and Decatur, Ala.
The issues at the heart of the impasse are similar to those that led to a four-week shutdown of Boeing's commercial aircraft assembly operations in the Pacific Northwest and Wichita, Kan., in September.
The machinists say Boeing has proposed ending retirement health care coverage for new employees and wants to eliminate caps on out-of-pocket expenses for medical premiums and copays. The workers argue that they should not be making concessions when the company posted $1 billion in net income for the last quarter.
"We're resolved in not allowing this company to take away from our future brothers and sisters," Quick said.
Beck said Boeing made an offer that was good for the company and its machinists.
The "average employee would have netted a substantial amount over the next three years," he said. "They would have had a more secure retirement as a result of boosts in pension benefits and savings plans. They and their families would have received top flight health benefits at a very modest cost."
Neither side would speculate as to how long the strike could last, but Quick said workers would stay off the job "one day longer than it takes" to get what they want.
Beck said he could not comment on Boeing's contingency plans.
Rocket launch delays are possible but no decisions have been made about scrubbing any planned launches, he said.
Boeing's Integrated Defense System unit primarily services the Air Force and NASA.
The company's Delta rocket program is based in Huntington Beach. The rockets are assembled at plants in Alabama and launched from Vandenberg and Cape Canaveral.
The commercial airline strike ended after machinists accepted a new contract that improved pension payouts and did not increase health care premiums.