Although construction employment is up 3.5 percent in the past year -- more than twice as fast as the rest of the workforce -- the sector has regained only about 13 percent of the 2.2 million construction jobs lost in the recession.
"There needs to be much stronger growth in construction employment to signal that economic growth has accelerated," Bronars said.
On Wednesday, two reports showed signs of optimism for the labor market.
Private payroll provider ADP said companies added 188,000 jobs in June, the largest gain since February and up from 134,000 in May. Construction employers added 21,000 jobs, a possible indication that a housing recovery is boosting job growth.
Also on Wednesday, the Labor Department reported the number of Americans filing unemployment claims fell 5,000 to a seasonally adjusted 343,000.
Last week, the S&P/Case-Shiller survey of 20 major metro areas reported a strong increase in average home prices with prices rising in all the cities it tracks; and the Commerce Department reported new home sales rose in May to the fastest pace in five years
Joe "JJ" Kinahan, chief strategist with TD Ameritrade, said the overall headline number in June's report was "fantastic".
"The market has held its tremendous overnight gains and all in all it looks to be very positive for equities," he said, while "the bond market has taken it on the chin" as ten-year yields have pushed to almost 2.65 percent.
His concern, he said, is "that we keep this great momentum going forward and that we have a better quality of jobs created."