Asked during Sunday's pageant in Las Vegas whether healthcare was a privilege or a right, Miss McCullough said: "I'm definitely going to say it's a privilege."
She added: "As a government employee, I'm granted healthcare and I see first hand that for one to have healthcare, you need to have jobs.
"We need to continue to cultivate this environment that we're given the opportunity to have healthcare as well as jobs to all American citizens worldwide."
Her remarks divided liberal-minded and conservative-minded viewers. Some were quick to criticise her stance.
Miss McCullough - who was born in Italy and was representing Washington DC - was also asked if she considered herself to be a feminist but said she preferred the term "equalism" and said men and women had equal opportunity in US workplaces.
"I don't really want to consider myself - try not to consider myself like this die-hard, you know, like, 'Oh, I don't really care about men'," said the contestant, who says she wants to see more women employed in government science roles.
Some people on social media supported her views.
Obamacare has been opposed by Republicans since it was first proposed in 2009.
Republicans say the law imposes too many costs on business and describe it as a "job killer", although the number of jobs in the healthcare sector has risen since it was introduced.
Opponents have also decried it as an unwarranted intrusion into the affairs of private businesses and individuals.