The Dem Progressives have no room to mock. Any aspect of eligibility they bring up the response should be “0bama never proved that one way or the other.” The RNC could run Marvin the Martian.
Leftists are hypocrites to the core they will definitely run stories about how Cruz is ineligible if he runs with absolutely straight faces and never mention Obama. Heck if he wins the nomination you expect the fedgov to begin investigating him.