Donald Trump let an audience member get away by insinuating that President Barack Obama is a Muslim and not even an American, as HNGN previously reportedWhat Trump probably did not realize was the impact his failing to correct the speaker at Rochester, N.H., might have on him and his presidential campaign.

In fact, this is not the first time that Trump has been openly skeptical about Obama's religion and nationality.

"He doesn't have a birth certificate. He may have one, but there's something on that, maybe religion, maybe it says he is a Muslim. I don't know. Maybe he doesn't want that," Trump had said to Fox News in 2011, according to CNN.

Meanwhile, presidential hopefuls across party lines condemned Trump for failing to chastise the man who had raised the issue.

"He knew, or he should have known, that what that man was asking was not only way out of bounds, it was untrue. He should have from the beginning repudiated that kind of rhetoric, that level of hatefulness," said Democratic frontrunner Hillary Rodham Clinton, according to Al Jazeera.

"If somebody at one of my town hall meetings said that, I would correct them and I would say, 'The president's a Christian and he was born in this country. Those two things are self-evident,'" said New Jersey Governor Chris Christie, adding that leaders had an "obligation" to correct all such statements, reported BBC News.

"Mr Trump isn't the first Republican politician to countenance these kind of views in order to win votes. That's precisely what every Republican presidential candidate is doing when they decline to denounce Mr. Trump's cynical strategy," said White House press secretary Josh Earnest, reacting to the incident, according to Al Jazeera.