In the final weeks of the 2016 campaign U.S. officials were frantically trying to get the American public to notice that elections systems in states across the country were under assault. A former U.S. official familiar with the intelligence says there were "massive alarms" going off about the scope of Russian attempts to breach voter databases.

The official says databases in key battleground states were at risk of being penetrated. The source mentioned that there were about five or six states, including Wisconsin and Florida. The official says some voter registration data may have been "exfiltrated" but that investigators weren't certain that information had been taken out of the systems. Furthermore, U.S. officials at the time were reluctant to talk about the breaches out of concern that doing so would reveal sources and methods.

Former Obama administration officials say that some states were accusing the Homeland Security Department (DHS) of trying to interfere in the election, and they adamantly warned federal officials against further comment about the vulnerabilities Russian hackers had exposed. In addition, former U.S. officials say some states were saying publicly that there hadn't been any breaches of voter databases, but those denials did not include attempts to breach contractor election systems used by some states.

Sources say some of the attacks were not sophisticated, and officials suspected that the hackers wanted to cause confusion and create enough doubt about the election systems to discourage people from voting. Officials in leadership positions at DHS during this period tell CBS News that they were trying to get the public to pay attention, but on the very day that officials blamed the Russians for interfering in the election, the "Access Hollywood" tape -- a decade-old video in which Mr. Trump could be heard making lewd comments about women -- drew attention away from the story.

Within DHS, top officials were angered and concerned that the message was being overshadowed. It was described as a sobering moment for U.S. officials who had made the decision to blame the Russians. This was a moment of historic significance, and yet it was being ignored in the aftermath of the "Access Hollywood" story. In the end, DHS offered cyber assistance to all 50 states, but some state elections officials were leery of federal assistance. DHS officials at the time insisted that what they were offering was simply "a move to the front of the line," should an election-related intrusion occur.

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Looking back, some former Obama administration officials express regret, although one source said, "I think we did all that we could." He was referring to whether they had done enough to stop Russian interference. Finally he said, "Before folks realized it was a real problem, it was a real problem."

Tuesday night, Florida officials released a statement to CBS News saying that "Florida's online elections databases and voting systems remained secure in 2016." The statement went on to say that the state has "multiple safeguards in place to protect against elections fraud and prevent any possible hacking attempts from being successful."

Florida says it's secured its databases and put in firewalls to protect information, and the state has "no indication that any unauthorized access occurred."

The state went on to say that it had no indication of hacking attempts, and it also pointed out that Florida voting is done on paper ballots, so election officials can refer to the original record, with an exception granted to voters with disabilities.

Florida officials spoke with the FBI about elections security at the end of Sept. 2016, and they said they had "a smooth and secure election in 2016."

A Wisconsin official said that after the news last year about voter database intrusions in Arizona and Illinois, the state conducted a review of its systems to assess security, which included asking the Department of Homeland Security to review that security. Officials say throughout that process they were told that if there had been some kind of attempt that they had detected that they would let them know. They have not alerted them of any attempts as of now. On Tuesday, Wisconsin officials sent out this election security reminder to local officials.

CBS News' Katie Ross Dominick contributed to this report.