Not true. I was part of those opposing Obama based on his background. He was naturalized as a U.S.citizen in 1983; formerly he was an Indonesian citizen.
See: the blog of Leo Donofrio, which began in December 2008 and ended March 2012. His arguments for a strict understanding of the Article II eligibility requirement for Natural born citizenship is amazing. I strongly suggest you read all four years worth of information. All of it is eye opening. Note: anyone who challenged Obamas claims received death threats; Cruz has not gotten to that point.
https://naturalborncitizen.wordpress.com/2008/12/