The man asked about the nation's "moral decay," pointing to the decision to light up the White House in rainbow colors to honor the high court's ruling.
"It was a sad day when I saw the capitol building all lit up in the rainbow colors," Randy DeLong said. "How will your faith have a positive effect? How will you light that faith to make changes?"
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Cruz, a vocal opponent of marriage equality, responded by saying that the rainbow display was an inherent sign that "our country is in a time of crisis."
He also reiterated his claims that the decision is "fundamentally illegitimate, lawless and unconstitutional."