The first available monthly indicator of the labor market is the "jobs plentiful" series in the Consumer Confidence Index (CCI) survey. Today, June's reading showed that 38.1% of respondents said so (chart). That's a slight uptick from May, and a relatively high reading. The "jobs hard to get response" ticked down to 14.1%, which is a very low reading.
The latter series is highly correlated with weekly initial unemployment claims and continuing claims (chart). These two weekly series edged up a bit in June raising concerns that the unemployment rate may be heading higher. However, the CCI survey data suggest that the unemployment rate probably remained at 4.0% during June.