A strike would put the World Series in jeopardy for the second time in less than a decade and leave the sport with an uncertain future.
"The baseball owners and the baseball players must understand that if there is a work stoppage, a lot of fans are going to be furious," President Bush said. "And I'm one of them."
The players insisted they do not want to strike, but said a strike date was needed to give a boost to stalled negotiations.
There had been optimism earlier this week that negotiations were moving forward, but progress has been minimal on the key issue of a luxury tax that would be imposed on teams with the highest payrolls.
So a deadline was set that has baseball headed for its ninth work stoppage since 1972.
"The players are committed to reaching a fair and equitable agreement, one which takes into account their views and not just those of the owners," union chief Donald Fehr said. "Needless to say, we are prepared to meet and bargain with the owners' representative until an agreement is reached."
The union announced that the vote to strike, made via a conference call, was unanimous and that 57 players participated in the discussion.
"The purpose to set a strike date is to speed up negotiations," said Joe Girardi, player representative for the Chicago Cubs. "All unions used to have to set a strike date and you hope it gets you over the top to get negotiations.
"It's not to strike because all of us want to play the game and that's what we love to do. It's just to get a deal done."
Arizona Diamondbacks first baseman Mark Grace also tried to stress that a strike is not definite.
"It's just a deadline, just like you have a deadline. All of us live on deadlines," he said. "It doesn't mean we will absolutely go on strike. I can't tell you a player that wants to go on strike. None of us do."
The two sides did not set a meeting for Friday, the first time in almost a month they had not had a session. Rob Manfred, baseball's vice president of labor relations, said that management is "ready and willing to meet at any time."
A walkout at the start of the Labor Day weekend would leave the remainder of the season in doubt and bring about the possibility the playoffs and World Series would have to be called off. Baseball was left without a champion in 1994 when the players struck late in the season.
"It's very important for these people to get together," Bush said in reacting to the news that a strike date had been set. "They can make every excuse in the book not to reach an accord. It is bad for them not to reach an accord."
Prior to becoming governor of Texas, Bush was part of the ownership group of the Texas Rangers.
Hope had grown in recent weeks that a settlement might be reached when the players made a proposal regarding testing for steroids. But the key issues involving revenue and how it is shared does not appear to be anywhere near a resolution.
Players and owners reportedly have reached agreement on minimum salaries and financing of a benefit plan.
The current owners' proposal would impose a 50 percent tax that part of a payroll that exceeds $98 million. A report in the New York Times Friday said owners had increased that amount to $102 million.