"We either have an incredibly inept administration, or they're in on this somehow or another," Perry had said Sunday on ABC's "This Week." "I mean I hate to be conspiratorial, but I mean how do you move that many people from Central America across Mexico and then into the United States without there being a fairly coordinated effort?"
Bolduan asked Perry to re-evaluate that statement in the wake of his meeting with Obama in Austin.
"Do you really honestly believe, as you said in that interview last month, that the administration might be in on this somehow?" she asked on CNN's "New Day." "I mean, you're suggesting there's some kind of conspiracy here."
"No. What I'm suggesting is that this administration and their words and their actions, or the lack thereof, are part of the problem," Perry responded. "I think you're putting the words of conspiracy in my mouth, which I did not say."
"No, you actually did say the word 'I hate to be conspiratorial,'" Bolduan pressed.
"And I hate to be conspiratorial, I hate to be conspiratorial," the Texas governor grinned. "I did not say I was."
"How can you move that many people from Central America across Mexico and then into the United States without there being a fairly coordinated effort," Bolduan said, quoting the governor.
"I don't know," Perry said.
"I'm just asking, governor, because words matter, you know that," Bolduan said.
"I totally understand, but the real issue here rather than getting into a semantics battle is whether or not this president is going to lead this country," Perry dodged.
"Can you work hand in hand, though, with a President that you criticizes so harshly on an issue that is so important to you?" Bolduan asked. "Can you get past the politics?"
"I did today, so I suspect we will," the governor responded.
Perry had harsher words for Obama in an interview with Fox News' Sean Hannity that aired Wednesday night. The Texas governor equated the President's refusal to visit the Texas border to former President George W. Bush's handling of Hurricane Katrina.
This post has been updated.