From the IRS (https://www.irs.gov/taxtopics/tc753):

Exemption from withholding

An employee can also use Form W-4 to tell you not to withhold any federal income tax. To qualify for this exempt status, the employee must have had no tax liability for the previous year and must expect to have no tax liability for the current year. A Form W-4 claiming exemption from withholding is valid for only the calendar year in which it's furnished to the employer. To continue to be exempt from withholding in the next year, an employee must give you a new Form W-4 claiming exempt status by February 15 of that year. This date is delayed until the next business day if it falls on a Saturday, Sunday, or legal holiday. If the employee doesn't give you a new Form W-4 by February 15, withhold tax as if the employee is single or married filing separately with no other entries in step 2, 3, or 4. If the employee provides a new Form W-4 claiming exemption from withholding on February 16 or later, you may apply it to future wages but don’t refund any taxes withheld while the exempt status wasn’t in place.<

So, one may file a W-4 annually that declares that one is exempt from withholding. However, to do so, one must have had "no tax liability" for the previous year. I suppose that if one were to fail to file an income tax form, one may slip under the vigilance of the IRS, but wouldn't the employer file information that would indicate that the employee did indeed receive income (i.e. may have a tax liability) each year? I'm not sure if "no tax liability" means taxes owed equals zero, which could happen in a number of circumstances even in cases when one has earned an income (lots of deductions, total income less than the personal exemption, et cetera) and rich people have lots of ways to make that exact situation happen year after year. That's how they stay rich.

So, yeah I guess one could declare exemption, but the point being made is that for many people, their willingness to take a risky option like flouting IRS rules may be OK for themselves, but they may be looking at some little mouths to feed and are unwilling to put THEIR future in jeopardy in order to show defiance.

My own recommendation is for government workers to either stop showing up or as Homer Simpson says "go to your job every day and do it really half-assed". Once the toilet paper stops getting changed, trash doesn't get emptied and payroll stops getting processed, the government would lose a lot of ability to enforce its authority rather quickly. The revolution doesn't need to be televised. It could happen by simply sitting on your sofa.

But, "then other people would take those jobs". Sure, but an effective marketing campaign could make that unpopular. If one were to travel to 1940 and tell the people living then that cigarettes would someday be largely illegal and decidedly uncool , the people living then would think that you're a kook. Making government work uncool could be just as easy.