Research by an organization called Project: Time Off led to the discovery of these modern-day workplace martyrs. Project: Time Off has been attempting to convince American workers and employers that it is a bad idea not to use earned time off, that it leads to lower productivity and lower worker engagement. As the organization says on its website, "We aim to shift culture so that taking time off is understood as essential to personal wellbeing, professional success, business performance, and economic expansion."

Perhaps the branding of people who work too hard and play too little as "work martyrs" will focus more attention on the issue. When Project: Time Off analyzed the results of responses from 5,641 employees about their work habits, the result was that 4 out of 10 say they want to be viewed as work martyrs by their bosses. One of their key tactics to attain this dubious distinction was to refuse to take off as much time as they had in the vacation bank.

Related: PTO 'banks' quickly becoming the norm

But this new martyrdom is a much more private affair than most historic martyrdoms. While these people want their bosses to view them in this light, 86 percent of them said they definitely did not want their families to be aware of their sacrifices.

And because the study reveals that millennials comprise the overwhelming majority of work martyrs, they will likely be attempting to keep this secret martyrdom from their families for years to come.

Project: Time Off broke out responses by millennials and baby boomers to demonstrate the much greater need millennials have to be seen by the boss as a martyr to the job. Nearly half (48 percent) of millennials say they believe it's good to be seen as a martyr at work, compared to 32 percent of boomers. Among the other comparisons from the data:

• 43 percent of millennials consider themselves work martyrs, compared to 29 percent of all other workers.

• Millennials are much more insecure about their job security, with 26 percent saying they forego time off so they won't jeopardize a promotion, compared to 9 percent of boomer work martyrs.

• 30 percent of millennial work martyrs say they don't take time off because they want to be seen as totally dedicated to the job, compared to 15 percent of boomer work martyrs.

• 27 percent of millennial work martyrs say they feel guilty about taking time off, compared to 12 percent of boomer work martyrs.

It's bad enough that so many millennials are afraid to take their full vacation and paid timeoff days to regenerate, Project: Time Off says. But more concerning is the fact that, as millennials move into management, they will pressure their direct reports to follow their poor example.

"The 'entitled millennial' narrative is dead wrong when it comes to vacation. As the largest generation in the workforce, one that is now stepping into management, millennials are developing vacation attitudes that will define and negatively affect America's work culture," says Project: Time Off Senior Director and report author Katie Denis. "The circumstances of the millennial experience — the Great Recession and its aftershocks, growing student debt, and an always-connected lifestyle — have created a perfect storm for their work martyr behavior."