Thousands of teachers gathered at the Capitol to ask lawmakers to override the vetoes.
In a video posted to YouTube on Sunday, Bevin backtracked and apologized for the "unintended consequences" of his words.
Republican Senator Whitney Westerfield thanked the governor saying, "Thank you, for making a public apology, taking responsibility for your words and recognizing the fear and hurt experienced by educators understandably worries about the future". But clearly a tremendous number of people did not fully appreciate what it was that I was communicating or what it was that I was trying to say, and I hurt a lot of people.
On Saturday, one day after the teachers' one-day strike, the Republican-led Kentucky House swiftly approved two resolutions condemning Bevin's comments in a sharp bipartisan rebuke. Representatives in his office did not respond to an email seeking comment.
Teachers were urged to wear black Monday, calling the movement "Black Out Bevin".
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The protests in Kentucky follow teachers' demonstrations across several states, demanding higher pay and more funding for education.
"Children were harmed - some physically, some sexually, some were introduced to drugs for the first time - because they were vulnerable and left alone", he said on Friday.
Teachers had flocked to Frankfort on Friday to rally for public education and call for the governor's vetoes of the tax reform and budget bills to be overridden.
"The bottom line is that's one day".
Nearly immediately, Bevin and his remarks were sharply criticized, according to the Louisville Courier Journal. "We were there with the overwhelming support and encouragement of our parents who know that we care about every student in our classes".
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"The disgusting comments by Gov. Bevin insinuating that a peaceful protest by teachers would lead to sexual assault are reprehensible", Wise wrote.
And after watching the video Sunday, she said, 'Seriously? In Arizona, protests and walkouts triggered Republican Gov. Doug Ducey's promise of a 20 percent raise by 2020. Education groups argue that less generous retirement funds may dissuade younger people from becoming teachers.
In his apology on Sunday, Bevin apologized several times and said that his remarks had been misunderstood.
"I don't want to be out of my classroom". We need each other. So it's odd that he felt justified in vetoing a recent bill that would increase funding for schools. He says he is considering a special session, partly because lawmakers did not pass school safety legislation.
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