Updated at 10:40 p.m. ET:

Sen. Rand Paul, R-Ky., another potential presidential nominee, told radio host Laura Ingraham on Monday that he thought most vaccinations should be voluntary, The Washington Post reports.

The senator, an ophthalmologist away from his political life, later told CNBC that vaccination should be encouraged, but that he also had heard of children developing "profound" mental impairment after being vaccinated.

Original Post:

As the country deals with what the Centers for Disease Control and Prevention is calling a record number of measles cases, New Jersey Gov. Chris Christie, a rumored 2016 presidential contender, has jumped into the national debate on vaccines.

Christie was visiting a facility in England of an American company that makes a flu vaccine. Given that the current measles outbreak has been driven by unvaccinated children, a reporter asked, did he think Americans should vaccinate their kids?

Christie said he and his wife decided to vaccinate their kids, and that is "the best expression I can give you of my opinion."

But then he went on to seemingly allow for some wiggle room: "I also understand that parents need to have some measure of choice in things as well so that's the balance that the government has to decide. But I can just tell people from our perspective, Mary Pat and I have had our children vaccinated and we think it's an important part of making sure we protect their health and the public health."

Quickly, Christie was criticized on Twitter by Dan Pfeiffer, a top adviser to President Obama. Pfeiffer called on Christie to clarify his statement.

Obama, he noted, has said that without dispute, science has validated vaccines.

"There is every reason to get vaccinated, but there aren't reasons to not," Obama told NBC News.

Pfeiffer said it was "important that responsible leaders speak with one voice."

Christie's office quickly clarified what the governor meant.

His spokesman, Kevin Roberts, said in a statement emailed to the press that Christie "believes vaccines are an important public health protection and with a disease like measles there is no question kids should be vaccinated."

The balance he was talking about has to do with different states requiring "different degrees of vaccination," the statement said.

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