By Heidi N. Moore, contributor

The feeling has become familiar. The adrenaline pumping, the heart beating hard, the fight-or-flight response set to kick in.

Yes, it is the day for employment numbers. Just to catch up, private-sector jobs grew by 83,000 and total payrolls declined by 125,000. The all-inclusive jobless rate is 16.6%, roughly flat with last month. And 6.8 million have been unemployed for 27 weeks or more, making up 45% of the unemployed.

Every month the drama restarts anew: Will the jobs report indicate a reverse in the recession? Will private-sector jobs reveal the return of corporate confidence? Will this be the month that our current malaise starts to look more like a recovery and less like a double-dip recession?

It’s crucial information to know. Unfortunately, making sense of the job report for the purpose of forecasting economic trends is as difficult and crude a method as the fortunetellers of old who predicted tribal events by reading the entrails of slaughtered animals. It’s messy, and we’re still no wiser as to where we are or what’s coming next.

Almost anything could interfere with the purity of employment numbers, because they are largely collected from applications for unemployment insurance. More Americans are falling out of the government counting as their unemployment benefits run out. And the fact that hiring of temporary Census workers is enough to significantly skew the employment numbers is reason enough to start thinking about other ways to gauge our economic health.

Deutsche Bank’s economic team has a solution: Find out whether people are participating in the economy, forget employment numbers. Check out taxes.

This week, Deutsche’s economic team put in another plug for its long-standing theory that it is more productive to see how much in tax income companies are withholding in order to get a sense of how much money is really swirling in the job market. (It wouldn’t work to track how much in taxes people actually pay, because the data is not regular, and also because 47% of Americans don’t pay federal taxes.) Here’s what the team said:

“We have long emphasized the importance of monitoring withholding tax receipts as a gauge of health in the labor market. This data series is particularly useful because it is timely and not subject to revision, although it does not differentiate whether income trends are due to changes in hiring, wages or hours worked. As a result, tax receipts are more useful as a proxy for household income than employment. In some sense, however, we would argue that the income trend is more important than the hiring trend, because the particular source of the income is less relevant than the fact that it is actually being generated.”

Tax receipts are more of a lagging indicator, but they don’t lag by all that much. In addition, they’re updated daily by the Treasury Department (under “Federal Tax Deposits”) and monthly, so it’s not necessary for investors to spend a week every month shivering in anticipation of numbers releases as we do with the employment figures. Treasury also provides a handy comparison of tax receipts every month between 1980 and 2010.

So what do the tax receipt numbers show? The June numbers aren’t out yet. But some back-of-the-envelope calculations show the picture in 2010 to be sunnier than 2009. May 2010’s tax receipts were fully 25% higher than those of May 2009. The tax receipts for January-May 2010 are 3.9% higher than they were for 2009.

Counting tax receipts won’t make our economic picture perfect. But they are an intriguing statistic to add to the mix.

–Heidi Moore is Sweeping the Street for the two weeks that Colin Barr is on vacation.