The airline, whose advertising slogan is "fly the friendly skies", was also ridiculed on social media as the incident became a symbol of growing discontent with the way some air passengers are treated. Forty-four percent of respondents who said they'd heard about United recently claimed they'd choose the more expensive American flight with a layover, according to the poll.
The aggressive removal of Dao left him with a concussion and a broken nose last Sunday.
As the PR disaster for United Airlines continues to rage on in the aftermath of a passenger being forcibly dragged off a flight, the airline is taking steps to ensure it doesn't happen again.
Almost a week since the incident, United is still dealing with the backlash.
When the news of Dao's forced removal from the flight came out, shares in United Continental, the parent company of United Airlines, fell by almost four per cent.
United Airlines has reportedly been reviewing several of its policies after a video leaked six days ago of officers violently booting a passenger from one of its flights. The 30 percent of respondents who said they hadn't heard about the airline recently were split almost 50-50 when it came to identical United or American flights.
"This violent incident should never have happened and was a result of gross excessive force by Chicago Department of Aviation personnel", the union said.