Romney was in danger of having his position on FEMA defined by the Obama campaign when the Republican repeatedly refused to answer questions from a reporter about his position earlier this week.
Similarly, Obama refused to answer questions last week from a local reporter in Colorado about whether his administration denied help to Americans under siege in Benghazi.
"We are finding out exactly what happened," Obama told KUSA-TV. "I guarantee you that everybody in the state department — our military, CIA, you name it, had the number one priority making sure that people were safe. These are our folks and we're going to find out exactly what happened, but what we're also going to do is make sure that we are identifying those who carried out these terrible attacks."
The day after the Libya attack, Obama said it was one in a number of "acts of terror" against the United States.
But then he and administration officials repeatedly suggested or said that it probably wasn't a terrorist attack, and instead was the result of an uprising due to an inflammatory anti-Islamic YouTube video that led to protests in Cairo, Egypt.
Rubio, who visited Libya last year and also sits on the Senate's Foreign Relations Committee, said the administration's response made no sense because Libyans are among the least likely to rise up against the United States.
"I was shocked by that because it didn't mesh with anything I knew about Libya," Rubio said.
Crediting CNN and "open-source reporting," Rubio said it became quickly apparent that the Benghazi attacks were coordinated, occurred over a long period of time and involved heavy weapons. Yet the administration kept talking about the YouTube video.
"That leads you to conclude one of two things: Either they're incompetent because they couldn't analyze all that," Rubio said. "Or there's something they didn't want to know about because it's against their political narrative — that al-Qaida's on the run and bin Laden died."
Rubio said there's a chance Obama's administration "underestimated the security risk in Libya because they didn't think terrorism was there and that it somehow didn't pose a threat."
Rubio said Democrats seem more invested in classifying information and delaying public hearings this election season.
Obama, in his Denver interview, suggested that wasn't the case.
"The election has nothing to do with four brave Americans getting killed and us wanting to find out exactly what happened," he said. "Nobody wants to find out more what happened than I do."
But that won't happen in the U.S. Senate until after Nov. 6.