Employee withholding taxes are a better indication of employment, cover most of the population every 2 weeks, and unlike estimates from the BLS, aren't distorted by adding fudge factors to get the numbers you want.
The problem with using withholding taxes is that the numbers could end up being far more skewed than you believe the BLS numbers to be. A large portion of the population works more than one job. By counting the number of people getting paychecks, even if you get the amount that they're getting paid, you risk strongly over-counting the number of people employed to one degree or another. Someone working a full-time job and a part-time job could be counted as two people employed, while someone working three part-time jobs could count as three people employed.
The BLS numbers aren't perfect, but they're the best information that we have. The tax-based numbers wouldn't go back more than a few years if we tried to start using them, so a new program to keep that information (and the highly individualized data associated with it) would have to start, run probably at least a decade, and might then be able to start producing useful numbers that could be published.
It would still be missing critical data, though: why people are unemployed. It only captures who isn't working. It doesn't include anything about those who went to school, stayed at home to be a parent, stay at home or cut back hours to care for an ailing family member, retire, or go on disability. It also misses people who own their own business with no employees, paying their taxes quarterly instead of monthly or biweekly, and one has to make estimates of how many of those are still in operation in between, and even with those numbers, many of them have separate jobs.
The end result is less, and probably muddier, data than we have now.
Withholding taxes are down, even as the "official" unemployment rate drops and more people enter the workforce. What that means is that people are making less money, good full-time jobs are being replaced by crap full-time, part-time, or no jobs.
That doesn't seem to be the case. According to the Treasury's monthly report (the latest available is for May 2016), individual income tax revenue for the current fiscal year is up over the same period in 2015, with $1.038 trillion this fiscal year compared to $1.015 trillion last fiscal year, an increase of about 2.3%.
I searched for the withholding tax revenue and didn't see it, so I checked the report for January 2016, before most people have started paying whatever back taxes they owe, and the revenue was even stronger: a 3.2% increase over the same period the year prior. Maybe you have the actual withholding numbers, which I'd love to see if that were the case. The available evidence, though, contradicts your assertion.