Story highlights New Mexico Gov. Gary Johnson responded to comments Ted Cruz made Wednesday

"I think Donald Trump alienates more than half of the Republicans," he said

Washington (CNN) Libertarian Party nominee Gary Johnson said Thursday that Ted Cruz's call to "vote your conscience" essentially encouraged people to support the former New Mexico governor.

"He did say to vote for Gary Johnson, didn't he? And that was 'vote your conscience,'" he told CNN's Chris Cuomo on "New Day." "I certainly would uphold the Constitution."

On Wednesday, Cruz upset many Republican National Convention attendees when he refused to endorse the party's nominee, Donald Trump, and told the crowd to "vote your conscience."

Johnson is just polling points from being able to appear on the presidential debate stages this fall.

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