The Wells Fargo Economics Group recently reported that the latest figures indicate that the total value of construction spending put in place in the U.S. in May was down 0.8 percent, which means back-to-back dips for that reading.

The group's analysis says that this could lead to weak second quarter results overall, and that soft public spending bears much of the liability. Private residential construction spending dropped only 0.3 percent in May and is up 4.7 percent from May 2015. Private single-family figures were off for the third month in a row but spending on multifamily units increased for the month.

A statement from the group read, "Weakness in private single-family is a bit disconcerting, especially given recent declines in single-family housing permits. Although it's too early to tell if the recent U.S. bond rally resulting from the Brexit vote will keep long-term U.S. Treasury yields low, if sustained, we could see another refinancing wave, which will keep homeowners in place."

Also up for the month was construction spending on home improvements, which currently registers a 2.3 percent increase over May of last year.