"We're going to lose a lot of employees over this," said Cornell Beard, head of the local Machinists union district.
Many workers did not object to the vaccines as such, he said, but were staunchly opposed to what they see as government meddling in personal health decisions.
The union district has hired a Texas-based lawyer to assist employees and prepare potential lawsuits against the companies should requests for medical or religious exemptions to vaccination be denied.
A life-long Democrat, Beard said he would no longer vote for the party.
"They'll never get another vote from me and I'm telling the workers here the same thing."
The clock is ticking for companies that want to continue gaining federal contracts under an executive order by Democratic President Joe Biden, which requires all contractor employees be fully vaccinated against COVID-19 by December 8.
That means federal contract workers need to have received their last COVID-19 shot at least two weeks before the deadline to gain maximum protection, according to US government guidance.
The mandate has stirred protests from workers in industries across the country as well as from Republican state officials.
Opposition to the mandate could potentially lead to thousands of US workers losing their jobs and imperil an already sluggish economic recovery, union leaders, workers and company executives said.
More legal clashes are likely over how companies decide requests for vaccination exemptions.
For the companies, time is getting tight, although the Biden administration has signalled federal contractors will not have to immediately lay off unvaccinated workers who miss the December 8 deadline.
Under government guidance published on Monday, companies will have flexibility over how to implement the mandate, which may allow them to avoid mass firings.
"A covered contractor should determine the appropriate means of enforcement with respect to its employee," the guidance said.
For Boeing Co in the United States, more than 7000 workers have applied for religious exemptions and about 1000 are seeking medical exemptions, people familiar with the matter told Reuters.
That amounts to 6 per cent of the plane maker's roughly 125,000 US employees.
At a rally last week outside Boeing property in Auburn, many of the three dozen workers gathered in driving rain said they would rather be escorted off Boeing property on December 8 than take a vaccine.
Others said they would pursue early retirement.
"The mandate is illegal, immoral and impractical," said one veteran Boeing program analyst who attended the rally.
"We are standing together against a company and government trampling on our rights."
Many legal experts have said vaccine mandates in the interest of public health are legal.
The rebellion has put Boeing executives in a bind.
The company could lose skilled staff but must comply with a presidential order.
A Boeing spokesperson said the company was committed to maintaining a safe working environment for its employees.
The order's provision for religious and medical exemptions is causing more tension.
Two Textron workers who requested religious exemptions told Reuters the company's human resources representatives quizzed them on the name of their church leaders and asked detailed questions about their faith.
Textron declined to respond to questions but in a statement said it was obligated to comply with Biden's order and was taking steps to do so.
"Employees who are unable to receive the COVID-19 vaccination due to a medical condition or sincerely held religious belief are being provided an opportunity to request an accommodation from this requirement," Textron said.
Raytheon Technologies' CEO Greg Hayes last week warned the US defence firm will lose "several thousand" employees because of the mandate.
A group representing FedEx Corp, United Parcel Service Inc and other cargo carriers said it would be virtually impossible to have all their workforces vaccinated by the deadline.
