There are those who have wanted to do away with barring naturalized citizens from becoming president. California Governor Arnold Schwarzenegger was an impetus for that movement at that time. It failed.
However actual courts have ruled that Ted Cruz is a natural born citizen and no court has ruled that he doesn’t qualify as natural born.
The court challenges are to be continued.
“Illinois and New Hampshire Agree Ted Cruz is a Natural Born Citizen”
http://www.americanthinker.com/articles/2016/02/illinois_and_new_hampshire_agree_cruz_is_a_natural_born_citizen.html