The Ohio congressman made the comment during a private luncheon Tuesday sponsored by the Ripon Society, a Republican group.
"Given what we heard yesterday about the president's vision for his second term, it's pretty clear to me that he knows he can't do any of that as long as the House is controlled by Republicans," Boehner said, according to a transcript. "So we're expecting over the next 22 months to be the focus of this administration as they attempt to annihilate the Republican Party."
He also told those who attended the event that he thinks the goal of members of the Obama administration is "to just shove us into the dustbin of history."
FoxNews' Chad Pergram contributed to this report.