Economists tend to shy away from attaching too much significance to any one piece of data. But in this environment, with this jobs report, hyper-scrutiny may be warranted.

When hiring in May eked out its weakest gain in more than five years, the shock was enough to cement the Federal Reserve's decision to hold off on raising interest rates. Then came Brexit—the U.K.'s surprise vote to withdraw from the European Union—and global economic anxieties were unleashed.

The June jobs report will therefore take on even more importance than usual. Economists and policy makers will use it to determine whether the strongest part of the economy slowed sharply even before concerns over global growth intensified, or if the labor market was merely hit by a temporary soft patch.