MICHELLE WU is signaling that she won’t back down from a fight – but also would desperately like to avoid one. 

As she navigates the latest of the many big challenges of her eventful early months in office, Boston’s mayor is wrestling in real-time with the maxim that two seemingly contradictory things can both be true at the same time. 

Wu declared as part of her aggressive stance on combating COVID-19 that all municipal workers must be vaccinated by January 15 or face the loss of their job. It was a dialing up of the previous policy requiring all city workers to be immunized or undergo regular COVID testing. Public safety unions took the city to court over the new policy – but a judge rejected their challenge and said the new rules could take effect. 

But just before the deadline arrived, Wu said city workers would be given an additional week to comply with the policy. As that deadline approached, she blinked again and said they would now have until January 30. 

Call it the double (not so) secret probation of vaccine mandates.

The conundrum for Wu – who has endured the daily taunts of anti-vaccine-mandate protesters outside her Roslindale home – is that she wants to project strength and determination during an early test of her mayoral might, but is certainly not eager to see hundreds of first responders lose their jobs and set off all-out war with their unions. 

​​“The goal of this was not to punish anyone for how they might feel about vaccination but to ensure that our city workers are safe and that any resident interacting with our city workforce is safe,” Wu said on Monday on WBUR’s “Radio Boston.” “I don’t take this lightly,” she said of the mandate.

Globe columnist Joan Vennochi on Tuesday urged Wu to hold the line against municipal unions. “In the end, the battle over vaccines is a fight for the common good,” she wrote. The paper’s editorial board weighed in today with much the same message. 

The city is reportedly in talks with the main Boston police union over an agreement that would give officers two mental health wellness days in exchange for complying with the mandate and also allow any officers let go because of failure to meet the deadline to be rehired within a certain period of time. 

Some might wonder why the city has to trade additional days off for the vaccine requirement and argue that what union members get in exchange for the mandate is protection against a deadly virus.

“It’s a real test of her earlier leadership,” said Erin O’Brien, a UMass Boston political science professor, about Wu’s handling of the issue. She’s between “a rock and hard place. She wants them to come around, and is giving them extra time to do that. Her risk is that gets read as weakness by the unions.” 

Sam Tyler, the former president of the Boston Municipal Research Bureau, said there is a broader context for the showdown, pointing out that all four Boston police unions and the two unions representing Boston firefighters are negotiating new contracts with the city. The police contracts in particular will draw lots of attention, since Wu has vowed to pursue reforms in line with calls for increased accountability in law enforcement. 

“I think if she shows weakness here or backs off, that will influence negotiations and make it tougher for the city,” Tyler said. “There’s a lot more riding on this than just getting the firefighters to get a shot.”