The California-based company is an important technology provider to the US government and also has growing ambitions in healthcare.

Tensions could heat up as employees seek to return to the office. Both Google and Facebook have said they will require staff coming into work to be vaccinated, but their policies have not been fully tested with most still working from home. Google employees will be expected to come back three days a week from January 10, at which point vaccine requirements might threaten to become even more controversial.

Google is unlikely to back down from its demands, and internal employee gripes are unlikely to bloom into full protest among a significant number of staff. But other parts of the US economy face tougher choices. Slightly more than 70pc of adults have been fully vaccinated, and 80pc have had one shot. In one in five states, fewer than half of adults are fully protected. 

That could lead Biden to redouble efforts to demand vaccines, insisting that mandates are the only way to make it happen. Requirements for nursing home workers in New York brought vaccination rates up from 77pc to 92pc in a month, for example.

But businesses are already struggling to hold onto staff amid wage pressures and a red hot job market. Enforcing a potentially unpopular vaccine demand, and having to lose workers who do not comply, is the last thing they might need.

In their petition, employees said: “I believe Sundar’s Vaccine Mandate is deeply flawed.”

The letter adds: “Barring unvaccinated Googlers from the office publicly and possibly embarrassingly exposes a private choice as it would be difficult for the Googler not to reveal why they cannot return.”

“It justifies the principle of division and unequal treatment of Googlers based on their personal beliefs and decisions. The implications are chilling. Due to its presence as an industry leader, Google’s mandate will influence companies around the world to consider these as acceptable tradeoffs.”

The White House has ordered that all companies in the US with more than 100 staff must get their staff vaccinated, or implement a policy of regular testing, by January 4.

In July, Google chief executive Sundar Pichai said the tech giant would require vaccinations for those returning to the office, but had previously said those who did not want to get vaccinated could work remotely.